cp's OEIS Frontend

A377520 The sum of the divisors of n that are terms in A207481.

%I A377520 #7 Oct 31 2024 01:11:49
%S A377520 1,3,4,7,6,12,8,7,13,18,12,28,14,24,24,7,18,39,20,42,32,36,24,28,31,
%T A377520 42,40,56,30,72,32,7,48,54,48,91,38,60,56,42,42,96,44,84,78,72,48,28,
%U A377520 57,93,72,98,54,120,72,56,80,90,60,168,62,96,104,7,84,144,68
%N A377520 The sum of the divisors of n that are terms in A207481.
%C A377520 First differs from A284341 at n = 81 = 3^4: a(81) = 40, while A284341(81) = 121.
%C A377520 The number of these divisors is A377519(n), and the largest of them is A377518(n).
%H A377520 Amiram Eldar, <a href="/A377520/b377520.txt">Table of n, a(n) for n = 1..10000</a>
%F A377520 a(n) = A000203(A377518(n)).
%F A377520 Multiplicative with a(p^e) = (p^(min(p, e)+1) - 1)/(p - 1).
%F A377520 Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (p^((p+1)*s) - p^(p+1))/p^((p+1)*s).
%F A377520 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * Product_{p prime} (1 - 1/p^(p+1)) = 1.42145673335960701365... .
%t A377520 f[p_, e_] := (p^(Min[p, e] + 1) - 1)/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A377520 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i,1]^(min(f[i,1], f[i,2]) + 1) - 1)/(f[i,1] - 1));}
%Y A377520 Cf. A000203, A013661, A207481, A284341, A377517, A377518, A377519.
%K A377520 nonn,easy,mult
%O A377520 1,2
%A A377520 _Amiram Eldar_, Oct 30 2024