A255369 a(n) = (sigma(n)-n-1)*(2-mu(n)), where sigma(n) is the sum of the divisors of n and mu(n) is the Möbius function.

-1, 0, 0, 4, 0, 5, 0, 12, 6, 7, 0, 30, 0, 9, 8, 28, 0, 40, 0, 42, 10, 13, 0, 70, 10, 15, 24, 54, 0, 123, 0, 60, 14, 19, 12, 108, 0, 21, 16, 98, 0, 159, 0, 78, 64, 25, 0, 150, 14, 84, 20, 90, 0, 130, 16, 126, 22, 31, 0, 214, 0, 33, 80, 124, 18, 231, 0, 114

Offset: 1

Author

Wesley Ivan Hurt, May 04 2015

Keywords

• sign

Comments

a(n) = 0 if and only if n is prime. If n is semiprime, then a(n) = sopfr(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Antti Karttunen, Sequence plotted up to n=10000, showing the details better

Crossrefs

Cf. A000203 (sigma), A008683 (Möbius function), A001414 (sopfr).

Cf. A048050 (Chowla's function), A228483 (2-mu(n)).

Programs

Magma

[(SumOfDivisors(n)-n-1)*(2-MoebiusMu(n)): n in [1..80]]; // Vincenzo Librandi, May 05 2015

Maple

with(numtheory): a:=n->(sigma(n)-n-1)*(2-mobius(n)): seq(a(n), n=1..100);

Mathematica

Table[(DivisorSigma[1, n] - n - 1) (2 - MoebiusMu[n]), {n, 100}]

PARI

a(n)=(sigma(n)-n-1)*(2-moebius(n)) \\ Dana Jacobsen, May 13 2015

Perl

use ntheory ":all"; say +(divisor_sum($)-$-1)*(2-moebius($)) for 1..80;  # _Dana Jacobsen, May 13 2015

Formula

a(n) = A048050(n) * A228483(n) for n > 1, a(1) = -1.

Extensions

Formula corrected for case n=1 by Antti Karttunen, Feb 25 2018