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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

%I

%S -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,

%T 0,123,0,60,14,19,12,108,0,21,16,98,0,159,0,78,64,25,0,150,14,84,20,

%U 90,0,130,16,126,22,31,0,214,0,33,80,124,18,231,0,114

%N 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.

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

%H Antti Karttunen, <a href="/A255369/b255369.txt">Table of n, a(n) for n = 1..65537</a>

%H Antti Karttunen, <a href="/A255369/a255369.png">Sequence plotted up to n=10000, showing the details better</a>

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

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

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

%o (MAGMA) [(SumOfDivisors(n)-n-1)*(2-MoebiusMu(n)): n in [1..80]]; // _Vincenzo Librandi_, May 05 2015

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

%o (PARI) a(n)=(sigma(n)-n-1)*(2-moebius(n)) \\ _Dana Jacobsen_, May 13 2015

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

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

%K sign

%O 1,4

%A _Wesley Ivan Hurt_, May 04 2015

%E Formula corrected for case n=1 by _Antti Karttunen_, Feb 25 2018

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Last modified August 21 05:48 EDT 2019. Contains 326162 sequences. (Running on oeis4.)