A255369 - OEIS

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

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OFFSET

1,4

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

FORMULA

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

MAPLE

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