A359603 - OEIS

A359603

Dirichlet inverse of function f(n) = 1+(A003415(n)*A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

1, -4, -7, -21, -19, 30, -11, 51, -132, -164, -91, -11, -51, -588, -935, -5904, -451, -1402, -251, -5979, -7347, -13898, -2251, -25507, -12140, -27718, -99060, -174307, -11251, 11610, -15, 52653, 685, 2410, -1095, 24800, -71, -198, -2647, 53673, -631, 61020, -351, 94173, -20052, -21368, -3151, 207838

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..11550

Index entries for sequences related to primorial base

FORMULA

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} (1+A358669(n/d)) * a(d).

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

A358669(n) = (A003415(n)*A276086(n));

memoA359603 = Map();

A359603(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359603, n, &v), v, v = -sumdiv(n, d, if(d<n, (1+A358669(n/d))*A359603(d), 0)); mapput(memoA359603, n, v); (v)));

CROSSREFS

Cf. A003415, A276086, A358669, A359590 (parity of terms), A359604 [= a(n) mod 60].

Cf. also A359427, A359589.

Sequence in context: A220004 A367911 A368185 * A255512 A039959 A320663

Adjacent sequences: A359600 A359601 A359602 * A359604 A359605 A359606

KEYWORD

sign,easy

AUTHOR

Antti Karttunen, Jan 11 2023

STATUS

approved