This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385136 #10 Jun 20 2025 08:09:25
%S A385136 1,2,3,4,5,6,7,9,9,10,11,12,13,14,15,19,17,18,19,20,21,22,23,27,25,26,
%T A385136 28,28,29,30,31,39,33,34,35,36,37,38,39,45,41,42,43,44,45,46,47,57,49,
%U A385136 50,51,52,53,56,55,63,57,58,59,60,61,62,63,79,65,66,67,68
%N A385136 The sum of divisors d of n such that n/d is a cubefull number (A036966).
%H A385136 Amiram Eldar, <a href="/A385136/b385136.txt">Table of n, a(n) for n = 1..10000</a>
%F A385136 Multiplicative with a(p) = p and a(p^e) = (p^(e+1) - p^e + p^(e-2) - 1)/(p-1) for e >= 2.
%F A385136 Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^s + 1/p^(3*s)).
%F A385136 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * Product_{p prime} (1 - 1/p^2 + 1/p^6) = 1.022486596136980366... .
%t A385136 f[p_, e_] := (p^(e+1) - p^e + p^(e-2) - 1)/(p-1); f[p_, 1] := p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A385136 (PARI) a(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i,1]; e = f[i,2]; if(e == 1, p, (p^(e+1) - p^e + p^(e-2) - 1)/(p-1)));}
%Y A385136 Cf. A013661, A036966, A385005.
%Y A385136 The sum of divisors d of n such that n/d is: A001615 (squarefree), A002131 (odd), A069208 (powerful), A076752 (square), A129527 (power of 2), A254981 (cubefree), A244963 (nonsquarefree), A327626 (cube), A385134 (biquadratefree), A385135 (exponentially odd), this sequence (cubefull), A385137 (3-smooth), A385138 (5-rough), A385139 (exponentially 2^n).
%K A385136 nonn,easy,mult
%O A385136 1,2
%A A385136 _Amiram Eldar_, Jun 19 2025