A373362 - OEIS

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A373362

a(n) = gcd(A001414(n), A276085(n)), where A001414 is the sum of prime factors with repetition, and A276085 is the primorial base log-function.

0, 1, 1, 2, 1, 1, 1, 3, 2, 7, 1, 1, 1, 1, 8, 4, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 2, 1, 12, 2, 1, 1, 8, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 4, 17, 1, 1, 8, 1, 2, 1, 1, 2, 1, 1, 1, 6, 6, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 9, 1, 1, 4, 1, 1, 2, 2, 1, 8, 1, 1, 1, 20, 1, 2, 1, 12, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

As A001414 and A276085 are both fully additive sequences, all sequences that give the positions of multiples of some k > 1 in this sequence are closed under multiplication: For example, A373373, which gives the indices of multiples of 3.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

PROG

(PARI)

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

A002110(n) = prod(i=1, n, prime(i));

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

A373362(n) = gcd(A001414(n), A276085(n));

CROSSREFS

Cf. A001414, A002110, A276085.

Cf. A345452 (positions of even terms), A373373 (positions of multiples of 3).

Cf. also A082299, A373361, A373363, A373367.