cp's OEIS Frontend

A349755 Numbers k for which the 3-adic valuations of k and sigma(k) are equal, and that also satisfy Euler's criterion for odd perfect numbers (see A228058).

%I A349755 #22 Aug 27 2025 18:22:14
%S A349755 153,325,801,925,1525,1573,1773,1825,2097,2205,2425,2725,3757,3825,
%T A349755 3925,4041,4477,4525,4689,4825,5013,5725,6025,6877,6925,6957,7381,
%U A349755 7605,7825,7929,8125,8425,8577,8725,8833,9325,9549,9873,9925,10225,10525,10693,10825,10933,11425,11493,11737,12789,13189,13437,13525
%N A349755 Numbers k for which the 3-adic valuations of k and sigma(k) are equal, and that also satisfy Euler's criterion for odd perfect numbers (see A228058).
%C A349755 Obviously, all odd perfect numbers x, if such numbers exist at all, have to satisfy not only the famous condition given by Euler (see A228058), but also valuation(sigma(x), p) = valuation(x, p) for all odd primes p = 3, 5, 7, 11, etc. See also comments in A349752.
%C A349755 a(109), a(283), a(440) = 31213, 88837, 146461, are the first terms not occurring in A387162. - _Antti Karttunen_, Aug 27 2025
%H A349755 Antti Karttunen, <a href="/A349755/b349755.txt">Table of n, a(n) for n = 1..10000</a>
%H A349755 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A349755 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A349755 (PARI)
%o A349755 isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
%o A349755 isA349755(n) = (isA228058(n)&&valuation(sigma(n), 3)==valuation(n, 3));
%Y A349755 Intersection of A228058 and A349749.
%Y A349755 Cf. A387162 (subsequence).
%Y A349755 Cf. A000203, A007949, A349752.
%K A349755 nonn,changed
%O A349755 1,1
%A A349755 _Antti Karttunen_, Dec 02 2021