cp's OEIS Frontend

A332445 Numbers k of the form 4m+1 for which A087808(sigma(k)) is equal to 2*A087808(k).

%I A332445 #35 Feb 22 2020 18:02:39
%S A332445 2009,19377,37809,59373,74673,115677,270041,310329,354609,357309,
%T A332445 720425,732321,841437,2071737,2612269,3131149,3866461,3930929,5172093,
%U A332445 5593981,7118753,7903961,8224173,9327393,9438129,11452321,12708025,18857209,18861889,18875313,19110321,20278269,20709225,20950061,23963597,24895153
%N A332445 Numbers k of the form 4m+1 for which A087808(sigma(k)) is equal to 2*A087808(k).
%C A332445 Numbers k such that A332224(k) is equal to A087808(2*k) and k == 1 mod 4.
%C A332445 Notably, the only square among the first 299 terms is a(248) = 5808421369 = 76213^2. sigma(5808421369) = 5808497583 == 3 (mod 4) == 7 (mod 8). Of the remaining 298 terms < 2^33, 92 are such that sigma(k) == 6 (mod 8) and 206 are such that sigma(k) == 2 (mod 8), that is, are terms of A332227.
%C A332445 Question: Why the terms come in clusters? Compare also the scatterplots of A087808 and A332224, and a similar sequence A332465.
%H A332445 Antti Karttunen, <a href="/A332445/b332445.txt">Table of n, a(n) for n = 1..299; all terms <= 2^33</a>
%H A332445 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H A332445 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A332445 (PARI)
%o A332445 A087808(n) = if(n<1, 0, if(n%2==0, 2*A087808(n/2), A087808((n-1)/2)+1));
%o A332445 isA332445(n) = ((1==(n%4))&&(2*A087808(n)==A087808(sigma(n))));
%Y A332445 Intersection of A016813 and A332446.
%Y A332445 Cf. also A228058, A332227, A332465.
%Y A332445 Cf. A000203, A087808, A286357, A332224, A332225, A332458.
%K A332445 nonn
%O A332445 1,1
%A A332445 _Antti Karttunen_, Feb 14 2020