A342653 - OEIS

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A342653

a(n) = mu(A156552(n)), where mu is Möbius mu function.

1, -1, -1, 0, -1, 0, -1, 1, 0, 0, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 1, 1, 0, 1, 0, -1, 1, 1, 0, 0, 0, -1, -1, 1, 0, -1, 0, -1, 1, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, -1, -1, 0, 0, -1, 0, 1, 1, 0, 0, 1, 0, 1, 1, -1, 0, 1, 0, 1, 1, 1, 0, 1, 0, -1, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, -1, -1

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OFFSET

LINKS

Table of n, a(n) for n=2..105.

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A008683(A156552(n)).

a(p) = 0 for primes p > 3.

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};

A342653(n) = moebius(A156552(n));

CROSSREFS

Cf. A008683, A156552.

Cf. also A323243, A324104, A324105, A324119, A342655 (sigma, phi, tau, omega and bigomega similarly permuted).

Sequence in context: A174897 A316441 A190938 * A189166 A092079 A342877

Adjacent sequences: A342650 A342651 A342652 * A342654 A342655 A342656

KEYWORD

sign

AUTHOR

Antti Karttunen, Mar 18 2021

STATUS

approved