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A173441 Number of divisors d of n such that sigma(d) divides n. 8

%I

%S 1,1,1,1,1,2,1,1,1,1,1,4,1,1,1,1,1,2,1,1,1,1,1,4,1,1,1,2,1,3,1,1,1,1,

%T 1,4,1,1,1,1,1,2,1,1,1,1,1,4,1,1,1,1,1,2,1,4,1,1,1,5,1,1,1,1,1,2,1,1,

%U 1,1,1,4,1,1,1,1,1,2,1,1

%N Number of divisors d of n such that sigma(d) divides n.

%C From _Robert Israel_, Oct 11 2017: (Start)

%C a(n) >= 1 since d=1 is always included.

%C a(n) = 1 if n is in A000961.

%C a(n) > 1 if n is in A097603. The first n not in A097603 such that a(n) > 1 is 117. (End)

%H Robert Israel, <a href="/A173441/b173441.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(n) - A173442(n). - A-number inserted by _R. J. Mathar_, Mar 06 2010

%e For n = 12, a(12) = 4; divisors of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d):1, 3, 4, 7, 12, 28; sigma(d) divides n for 4 divisors d: 1, 2, 3, 6.

%p f:= proc(n) nops(select(t -> n mod numtheory:-sigma(t) = 0, numtheory:-divisors(n))) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Oct 11 2017

%o (PARI) a(n) = sumdiv(n, d, !(n % sigma(d))); \\ _Michel Marcus_, Oct 11 2017

%Y Cf. A000005, A000961, A097603, A173442.

%K nonn

%O 1,6

%A _Jaroslav Krizek_, Feb 18 2010

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Last modified November 14 04:53 EST 2019. Contains 329108 sequences. (Running on oeis4.)