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.
%I A326070 #15 Jul 17 2021 11:24:07 %S A326070 2,3,5,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,26,28,29,30,31,32,33, %T A326070 34,35,36,37,38,39,40,41,42,43,44,46,47,48,51,52,53,54,55,56,57,58,59, %U A326070 61,62,64,65,66,67,68,69,70,71,72,73,74,76,77,78,79,80,82,83,85,86,87,88,89,91,92,93,94,95,96,97,100 %N A326070 Numbers k such that A325977(k) has the same sign as A325978(k). %C A326070 Here A325977(k) = A325973(k) - k and A325978(k) = k - A325974(k), where A325973(k) is the average of {sum of unitary divisors} and {sum of squarefree divisors} = (1/2) * (A034448(k) + A048250(k)) while A325974(k) is the average of {sum of non-unitary divisors} and {sum of nonsquarefree divisors} = (1/2)*(A048146(k) + A162296(k)). Only if signs of A325977(k) and A325978(k) are equal can their difference A325978(k) - A325977(k) = (k - A325974(k)) - (A325973(k) - k) = 2k - (A325973(k) + A325974(k)) = 2k - A000203(k) = A033879(k) be zero, which happens when k is a perfect number (in A000396). %H A326070 Antti Karttunen, <a href="/A326070/b326070.txt">Table of n, a(n) for n = 1..10000</a> %o A326070 (PARI) isA326070(n) = (sign(A325977(n))==sign(A325978(n))); \\ For other needed code, see under A325975. %Y A326070 Cf. A000203, A033879, A325963, A325973, A325974, A325975, A325977, A325978, A325981. %Y A326070 Cf. A326071 (complement), A326072, A000396 (a subsequence). %K A326070 nonn %O A326070 1,1 %A A326070 _Antti Karttunen_, Jun 07 2019