cp's OEIS Frontend

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

%I A173441 #23 Mar 28 2024 09:03:24
%S A173441 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 A173441 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 A173441 1,1,1,4,1,1,1,1,1,2,1,1
%N A173441 Number of divisors d of n such that sigma(d) divides n.
%C A173441 From _Robert Israel_, Oct 11 2017: (Start)
%C A173441 a(n) >= 1 since d=1 is always included.
%C A173441 a(n) = 1 if n is in A000961.
%C A173441 a(n) > 1 if n is in A097603.  The first n not in A097603 such that a(n) > 1 is 117. (End)
%H A173441 Robert Israel, <a href="/A173441/b173441.txt">Table of n, a(n) for n = 1..10000</a>
%F A173441 a(n) = A000005(n) - A173442(n). - A-number inserted by _R. J. Mathar_, Mar 06 2010
%F A173441 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{n>=1} 1/A009242(n) = 1.605582... . - _Amiram Eldar_, Mar 28 2024
%e A173441 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 A173441 f:= proc(n) nops(select(t -> n mod numtheory:-sigma(t) = 0, numtheory:-divisors(n))) end proc:
%p A173441 map(f, [$1..100]); # _Robert Israel_, Oct 11 2017
%t A173441 a[n_] := Select[Divisors[n], Divisible[n, DivisorSigma[1, #]]&] // Length;
%t A173441 Array[a, 100] (* _Jean-François Alcover_, Jun 05 2020 *)
%o A173441 (PARI) a(n) = sumdiv(n, d, !(n % sigma(d))); \\ _Michel Marcus_, Oct 11 2017
%Y A173441 Cf. A000005, A000961, A009242, A097603, A173442.
%K A173441 nonn
%O A173441 1,6
%A A173441 _Jaroslav Krizek_, Feb 18 2010