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.

A323528 Numbers whose sum of prime indices is a perfect square.

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%I A323528 #14 Jun 06 2020 01:16:59
%S A323528 1,2,7,9,10,12,16,23,38,51,53,65,68,77,78,94,97,98,99,104,105,110,125,
%T A323528 126,129,132,135,140,150,151,162,168,172,176,178,180,200,205,216,224,
%U A323528 227,240,246,249,259,288,298,311,320,328,332,333,341,361,370,377,384
%N A323528 Numbers whose sum of prime indices is a perfect square.
%C A323528 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The sum of prime indices of n is A056239(n).
%C A323528 Also Heinz numbers of integer partitions of perfect squares, where the Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A323528 Robert Israel, <a href="/A323528/b323528.txt">Table of n, a(n) for n = 1..10000</a>
%e A323528 10 is in the sequence because 10 = 2*5 = prime(1)*prime(3) and 1 + 3 = 4 is a square.
%p A323528 select(k-> issqr(add(numtheory[pi](i[1])*i[2], i=ifactors(k)[2])), [$1..400])[]; # _Alois P. Heinz_, Jan 22 2019
%t A323528 Select[Range[100],IntegerQ[Sqrt[Sum[PrimePi[f[[1]]]*f[[2]],{f,FactorInteger[#]}]]]&]
%o A323528 (PARI) isok(n) = {my(f=factor(n)); issquare(sum(k=1, #f~, primepi(f[k, 1])*f[k,2]));} \\ _Michel Marcus_, Jan 18 2019
%Y A323528 Complement of A323527.
%Y A323528 Cf. A000290, A001248, A026478, A056239, A112798, A323520, A323521, A323525, A323526.
%K A323528 nonn
%O A323528 1,2
%A A323528 _Gus Wiseman_, Jan 17 2019