cp's OEIS Frontend

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.

A347156 Sum of squares of distinct prime divisors of n that are < sqrt(n).

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%I A347156 #5 Aug 20 2021 22:52:18
%S A347156 0,0,0,0,0,4,0,4,0,4,0,13,0,4,9,4,0,13,0,4,9,4,0,13,0,4,9,4,0,38,0,4,
%T A347156 9,4,25,13,0,4,9,29,0,13,0,4,34,4,0,13,0,29,9,4,0,13,25,53,9,4,0,38,0,
%U A347156 4,58,4,25,13,0,4,9,78,0,13,0,4,34,4,49,13,0,29
%N A347156 Sum of squares of distinct prime divisors of n that are < sqrt(n).
%F A347156 G.f.: Sum_{k>=1} prime(k)^2 * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).
%t A347156 Table[DivisorSum[n, #^2 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 80}]
%t A347156 nmax = 80; CoefficientList[Series[Sum[Prime[k]^2 x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y A347156 Cf. A001157, A005063, A005066, A098002, A333806, A333808, A339353, A347157, A347158.
%K A347156 nonn
%O A347156 1,6
%A A347156 _Ilya Gutkovskiy_, Aug 20 2021