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.

A351447 Numbers k for which A003958(sigma(k)) = 2*A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

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%I A351447 #13 Feb 12 2022 14:18:15
%S A351447 2,98,120,136,312,520,672,888,1080,1120,1464,1480,1752,2440,2520,2808,
%T A351447 2912,2920,3420,3768,3848,4632,5880,6048,6280,6344,6552,6648,6664,
%U A351447 7512,7592,7720,7992,8181,8288,8892,9528,10104,10968,11080,12464,12520,12984,13176,13664,14712,15288
%N A351447 Numbers k for which A003958(sigma(k)) = 2*A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
%C A351447 Numbers k such that A351442(k) = 2*A003958(k).
%C A351447 In contrast, numbers x for which A064989(sigma(x)) = 2*A064989(x) seem to consist just of {2} followed by A005820: 2, 120, 672, 523776, ..., etc, which (also) contains as its subsequence all the odd terms of A336702 multiplied by 2.
%H A351447 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A351447 (PARI)
%o A351447 A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
%o A351447 isA351447(n) = (A003958(sigma(n))==2*A003958(n));
%Y A351447 Cf. A000203, A003958, A064989, A351442.
%Y A351447 Subsequences: A005820 (3-perfect numbers), odd terms of A336702 doubled, the terms of A351443 doubled (2, 98, 81810, ...), A351448 (odd terms in this sequence).
%K A351447 nonn
%O A351447 1,1
%A A351447 _Antti Karttunen_, Feb 12 2022