cp's OEIS Frontend

A382788 The sum of divisors of n that are numbers whose number of divisors is a power of 2.

%I A382788 #16 Apr 26 2025 03:33:14
%S A382788 1,3,4,3,6,12,8,11,4,18,12,12,14,24,24,11,18,12,20,18,32,36,24,44,6,
%T A382788 42,31,24,30,72,32,11,48,54,48,12,38,60,56,66,42,96,44,36,24,72,48,44,
%U A382788 8,18,72,42,54,93,72,88,80,90,60,72,62,96,32,11,84,144,68,54
%N A382788 The sum of divisors of n that are numbers whose number of divisors is a power of 2.
%C A382788 First differs from A033634 at n = 32.
%C A382788 The sum of the terms of A036537 that divide n.
%C A382788 The number of these divisors is A372380(n) and the largest of them is A372379(n).
%H A382788 Amiram Eldar, <a href="/A382788/b382788.txt">Table of n, a(n) for n = 1..10000</a>
%F A382788 Multiplicative with a(p^e) = Sum_{k = 0..floor(log_2(e+1))} p^(2^k-1).
%F A382788 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 + Sum_{k>=1} a(p^k)/p^(2*k)) = 1.13143029377358401678... .
%t A382788 f[p_, e_] := Sum[p^(2^k-1), {k, 0, Floor[Log2[e + 1]]}]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A382788 (PARI) a(n) = my(f = factor(n), p = f[,1], e = f[,2]); prod(i = 1, #p, sum(k = 0, exponent(e[i]+1), p[i]^(2^k-1)));
%Y A382788 Cf. A000523, A033634, A036537, A372379, A353900, A372380.
%K A382788 nonn,easy,mult
%O A382788 1,2
%A A382788 _Amiram Eldar_, Apr 05 2025