A353364 - OEIS

A353364

Inverse Möbius transform of A332814.

0, 1, -1, 1, 1, -1, -1, 2, -1, 2, 1, -2, -1, -1, 1, 2, 1, 0, -1, 3, -2, 2, 1, -2, 1, -1, -2, -2, -1, 1, 1, 3, 1, 2, -1, -1, -1, -1, -2, 4, 1, -2, -1, 3, 2, 2, 1, -3, -1, 3, 1, -2, -1, -2, 2, -2, -2, -1, 1, 2, -1, 2, -3, 3, -1, 1, 1, 3, 1, -2, -1, 0, 1, -1, 0, -2, 1, -2, -1, 5, -2, 2, 1, -4, 2, -1, -2, 4, -1, 3, -2, 3

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OFFSET

1,8

LINKS

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

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = Sum_{d|n} A332814(d).

For all n >= 1, a(A003961(n)) = -a(n), a(A000040(n)) = ((-1)^(n-1)).

PROG

(PARI)

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552

A332814(n) = { my(u=A156552(n)%3); if(2==u, -1, u); };

A353364(n) = sumdiv(n, d, A332814(d));

CROSSREFS

Cf. A003961, A156552, A332814.

Cf. also A353354, A353361, A353362.

Sequence in context: A189024 A304720 A057557 * A328390 A325599 A023520

Adjacent sequences: A353361 A353362 A353363 * A353365 A353366 A353367

KEYWORD

sign

AUTHOR

Antti Karttunen, Apr 15 2022

STATUS

approved