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 A380444 #28 Jul 02 2025 17:08:45
%S A380444 1,5,10,9,26,20,50,17,19,40,122,36,170,68,50,33,290,47,362,64,80,148,
%T A380444 530,68,51,200,46,100,842,100,962,65,164,328,110,99,1370,404,218,112,
%U A380444 1682,146,1850,196,104,580,2210,132,99,115,350,256,2810,128,202,164,428,904,3482,196,3722,1028,152,129,260,262,4490,400,608,208,5042,203,5330,1448,150,484
%N A380444 Sum of the nonprimes dividing n and the squares of the primes dividing n.
%C A380444 Inverse Möbius transform of A103164(n).
%F A380444 a(n) = sigma(n) - sopf(n) + sopf_2(n), where sopf_2(n) = Sum_{p|n, p prime} p^2.
%F A380444 a(n) = Sum_{d|n} d^tau(d^c(d)), where c = A010051.
%F A380444 a(n) = A023890(n) + A005063(n).
%F A380444 a(p^k) = (p^(k+1)+p^3-2*p^2+p-1)/(p-1) for p prime, k >= 1. - _Wesley Ivan Hurt_, Jul 02 2025
%e A380444 a(12) = 1 + 2^2 + 3^2 + 4 + 6 + 12 = 36.
%t A380444 Table[DivisorSigma[1, n] + Sum[p (p - 1), {p, Select[Divisors[n], PrimeQ]}], {n, 100}]
%Y A380444 Cf. A000005 (tau), A000203 (sigma), A005063, A008472 (sopf), A010051, A023890, A103164.
%K A380444 nonn,easy
%O A380444 1,2
%A A380444 _Wesley Ivan Hurt_, Jun 21 2025