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.

A063900 Numbers k such that sum of proper divisors or aliquot parts of k^2 (excluding 1) is a square, or A048050(k^2) is a square.

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%I A063900 #23 Nov 17 2023 11:49:58
%S A063900 866,9271,18167,30887,39959,114607,119279,129911,153631,239111,343207,
%T A063900 517591,582583,602159,607340,1202282,1397863,1729999,1920647,2533183,
%U A063900 2547119,2558183,5740127,7122959,9379871,10218407,10891103,13549399
%N A063900 Numbers k such that sum of proper divisors or aliquot parts of k^2 (excluding 1) is a square, or A048050(k^2) is a square.
%H A063900 Amiram Eldar, <a href="/A063900/b063900.txt">Table of n, a(n) for n = 1..100</a> (terms 1..55 from Harry J. Smith)
%H A063900 Passawan Noppakaew and Prapanpong Pongsriiam, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Pongsriiam/pong43.html">Product of Some Polynomials and Arithmetic Functions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.
%t A063900 chowla[n_] := DivisorSigma[1, n] - n - 1; aQ[n_] := IntegerQ@Sqrt@chowla[n^2]; Select[Range[10^6], aQ] (* _Amiram Eldar_, Aug 30 2019 *)
%o A063900 (PARI) s(n)=sigma(n)-n-1;
%o A063900 for(n=1,10^8, if(issquare(s(n^2)),print(n)))
%o A063900 (PARI) s(n)=sigma(n) - n - 1
%o A063900 { n=0; for (m=1, 10^9, if(issquare(s(m^2)), write("b063900.txt", n++, " ", m); if (n==55, break)) ) } \\ _Harry J. Smith_, Sep 02 2009
%Y A063900 Cf. A008847, A048050.
%K A063900 nonn
%O A063900 1,1
%A A063900 _Jason Earls_, Aug 29 2001
%E A063900 a(19)-a(28) from _Harry J. Smith_, Sep 02 2009