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A325376 Terms k of A228058 such that gcd(k - A048250(k), A162296(k) - k) = A162296(k) - k.

%I A325376 #16 Jun 18 2019 07:24:09
%S A325376 153,477,801,1773,2097,2421,3725,4041,4689,4753,5013,5337,6309,6957,
%T A325376 7281,7929,8577,8725,9549,9873,11225,11493,13437,14357,14409,14733,
%U A325376 15381,17001,17973,18621,19269,19917,21213,21537,23481,24777,25101,25749,26073,26225,26721,27369,28989,29161,29313,29961,31225,32229,32553,33849
%N A325376 Terms k of A228058 such that gcd(k - A048250(k), A162296(k) - k) = A162296(k) - k.
%C A325376 Also, terms of this sequence are A228058(k) for all such k that A325375(k) = A325320(k).
%C A325376 In range 1 .. 2^27 there are no such terms k of A228058 that gcd(k-A048250(k), A162296(k)-k) = k - A048250(k).
%C A325376 If any odd perfect number exists, then it must occur in this sequence, but should also satisfy the other condition given above.
%H A325376 Antti Karttunen, <a href="/A325376/b325376.txt">Table of n, a(n) for n = 1..12532</a>
%H A325376 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%o A325376 (PARI)
%o A325376 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A325376 A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
%o A325376 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 A325376 k=0; n=0; while(k<100,n++; if(isA228058(n) && (gcd(n-A048250(n),A162296(n)-n) == A162296(n)-n),k++; print1(n,", ")));
%Y A325376 Cf. A048250, A162296, A228058, A325313, A325314, A325320, A325375, A325822.
%K A325376 nonn
%O A325376 1,1
%A A325376 _Antti Karttunen_, Apr 22 2019