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.

A227476 Numbers whose sum of semiprime divisors (A076290) is a positive square.

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%I A227476 #26 May 10 2020 04:32:49
%S A227476 4,8,9,16,25,27,32,49,64,81,121,125,128,138,169,225,243,256,289,306,
%T A227476 343,361,426,512,516,529,625,644,675,729,841,918,961,975,1002,1024,
%U A227476 1032,1125,1140,1146,1150,1220,1230,1288,1305,1316,1331,1369,1681,1849,2025
%N A227476 Numbers whose sum of semiprime divisors (A076290) is a positive square.
%C A227476 Except for the number 1, the sequence A195942 (Zeroless prime powers (excluding primes)) is a subsequence of this sequence because the set of divisors of the numbers of the form p^m with p prime and m >= 2 contains only one semiprime divisor, p^2.
%C A227476 The subset of the nonprime powers is {138, 225, 306, 426, 516, 644, 675, 918, ...}.
%H A227476 Amiram Eldar, <a href="/A227476/b227476.txt">Table of n, a(n) for n = 1..10000</a>
%e A227476 138 is in the sequence because the divisors of 138 are {1, 2, 3, 6, 23, 46, 69, 138} and the sum of the semiprime divisors is 2*3 + 2*23 + 3*23 = 11^2.
%t A227476 semipSigma[n_] := DivisorSum[n, # &, PrimeOmega[#] == 2 &]; Select[Range[2000], (s = semipSigma[#]) > 0 && IntegerQ @ Sqrt[s] &] (* _Amiram Eldar_, May 10 2020 *)
%o A227476 (PARI) isok(n) = issquare(s = sumdiv(n, d, d*(bigomega(d)==2))) && (s>0); \\ _Michel Marcus_, Sep 16 2017
%Y A227476 Cf. A001358, A025475, A076290, A164722.
%K A227476 nonn
%O A227476 1,1
%A A227476 _Michel Lagneau_, Jul 13 2013
%E A227476 Definition corrected by _Michel Marcus_, Sep 16 2017