Cf. A372575 (rgs-transform), A372576 [a(n) mod 360], A373842 [= A003415(a(n))].

Cf. A373145 [= gcd(A003415(n), a(n))], A373361 [= gcd(n, a(n))], A373362 [= gcd(A001414(n), a(n))], A373485 [= gcd(A083345(n), a(n))], A373835 [= gcd(bigomega(n), a(n))], and also A373367 and A373147 [= A003415(n) mod a(n)], A373148 [= a(n) mod A003415(n)].

Other completely additive sequences with primes p mapped to a function of p include: A001222 (with a(p)=1), A001414 (with a(p)=p), A059975 (with a(p)=p-1), A341885 (with a(p)=p*(p+1)/2), A373149 (with a(p)=prevprime(p)), A373158 (with a(p)=p#).

Fully Completely additive with a(p^e) = e * A002110(A000720(p)-1).

This is a left inverse of A276086 ("primorial base exp-function"), hence the new name "primorial base log-function". When the domain is restricted to the terms of A048103, this works also as a right inverse, as A276086(a(A048103(n))) = A048103(n) for all n >= 1. - Antti Karttunen, Apr 24 2022

a(1) = 0, a(n) = (e1*A002110(i1-1) + ... + ez*A002110(iz-1)) for when n = prime(i1)^e1 * ... * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k) and A002110(k) (the k-th primorial) is the product of first k primes.

a(A276076(n)) = A351576(n). [Sequence reinterpreting factorial base representation as a primorial base representation]

Cf. A000040, A000720, A002110, A028234, A034386, A048103, A049345, A055396, A067029, A108951, A143293, A276154, A328316, A328624, A328625, A328768, A328832, A346105, A351576.

Cf. A036554 (positions of odd terms), A035263, A096268 (parity of terms).

Cf. A003159 (positions of even terms), A036554 (of odd terms), A035263, A096268 (parity of terms), A339746 (positions of multiples of 3, char.fun. A372573), A369002 (of multiples of 4, char.fun. A369001), A372575 (rgs-transform), A372576 [a(n) mod 360].

Positions of multiples of k in this sequence, for k=2, 3, 4, 5, 8: A003159, A339746, A369002, A373140, A373138.

Cf. A036554 (of odd terms), A035263, A096268 (parity of terms).

Cf. A372575 (rgs-transform), A372576 [a(n) mod 360].

Primorial base log-function: fully additive with a(p) = p#/p, where p# = A034386(p). a(1) = 0, a(n) = (e1*A002110(i1-1) + ... + ez*A002110(iz-1)) for n = prime(i1)^e1 * ... * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k) and A002110(k) (the k-th primorial) is the product of first k primes.

Primorial base log-function: fully additive with a(p) = p#/p, where p# = A034386(p).

a(1) = 0, a(n) = (e1*A002110(i1-1) + ... + ez*A002110(iz-1)) for n = prime(i1)^e1 * ... * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k) and A002110(k) (the k-th primorial) is the product of first k primes.

Name simplified, the old name moved to the comments - Antti Karttunen, Jun 23 2024

Primorial base log-function: fully additive with a(p) = p#/p, where p# = A034386(p). a(1) = 0, a(n) = (e1*A002110(i1-1) + ... + ez*A002110(iz-1)) for n = prime(i1)^e1 * ... * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k) and A002110(k) (the k-th primorial) is the product of first k primes.

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Cf. A003159 (positions of even terms), A036554 (of odd terms), A035263, A096268 (parity of terms), A369001, A339746 (positions of multiples of 3, XXX: Check!char.fun. A372573), A369002 (of multiples of 4, char.fun. A369001), A372575 (rgs-transform), A372576 [a(n) mod 360].

Cf. A003159 (positions of even terms), A036554 (of odd terms), A035263, A096268 (parity of terms), A369001, A369002 A339746 (positions of multiples of 3, XXX: Check!), A369002 (of multiples of 4), A372575 (rgs-transform), A372576 [a(n) mod 360].

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