cp's OEIS Frontend

A366990 The sum of divisors of n that are terms of A056166.

%I A366990 #8 Nov 02 2023 10:26:59
%S A366990 1,1,1,5,1,1,1,13,10,1,1,5,1,1,1,13,1,10,1,5,1,1,1,13,26,1,37,5,1,1,1,
%T A366990 45,1,1,1,50,1,1,1,13,1,1,1,5,10,1,1,13,50,26,1,5,1,37,1,13,1,1,1,5,1,
%U A366990 1,10,45,1,1,1,5,1,1,1,130,1,1,26,5,1,1,1,13
%N A366990 The sum of divisors of n that are terms of A056166.
%C A366990 The number of these divisors is A095691(n) and the largest of them is A366993(n).
%H A366990 Amiram Eldar, <a href="/A366990/b366990.txt">Table of n, a(n) for n = 1..10000</a>
%F A366990 Multiplicative with a(p^e) = 1 + Sum_{primes q <= e} p^q.
%F A366990 a(n) >= 1, with equality if and only if n is squarefree (A005117).
%t A366990 f[p_, e_] := 1 + Total[p^Select[Range[e], PrimeQ]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A366990 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(j = 1, f[i, 2], if(isprime(j), f[i, 1]^j)));}
%Y A366990 Cf. A005117, A056166, A095691, A366988, A366993.
%K A366990 nonn,easy,mult
%O A366990 1,4
%A A366990 _Amiram Eldar_, Oct 31 2023