A325822 - OEIS

%I #13 Jun 18 2019 07:24:27

%S 477,3725,29161,107797,166753,205409,500837,535277,780625,1610389,

%T 5649841,6968125,10292809,10633429,24231241,32771201,38322857,

%U 40028661,104861501,170384117,183593125,277405641,326081953,488265625,491716541,704531953,797338489,836737393,2053219321,2359421369,3012238153

%N Terms k of A228058 for which A325814(k) is a multiple of A034460(k).

%C Such terms A228058(n) that A325823(n) is a divisor of A325824(n).

%C If any odd perfect number exists, then it must occur in this sequence.

%C This is not a subsequence of A325376: 107797 is the first term that does not occur there.

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%o (PARI)

%o A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448

%o A034460(n) = (A034448(n) - n);

%o A048146(n) = (sigma(n)-A034448(n));

%o A325814(n) = (n-A048146(n));

%o 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 for(n=1,oo, if(isA228058(n) && !(A325814(n)%A034460(n)), print1(n, ", ")));

%Y Cf. A034460, A228058, A325376, A325812, A325814, A325823, A325824.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 23 2019