cp's OEIS Frontend

A325812 Numbers k such that gcd(A034448(k)-k, k-A048146(k)) is equal to abs(k-A048146(k)).

%I A325812 #16 Jun 18 2019 16:12:35
%S A325812 1,6,12,28,56,60,108,120,132,168,264,280,312,408,420,440,456,496,528,
%T A325812 540,552,696,700,728,744,756,760,888,984,992,1032,1128,1140,1188,1272,
%U A325812 1404,1416,1456,1464,1608,1704,1710,1752,1836,1896,1992,2052,2136,2328,2424,2472,2484,2568,2616,2646,2712,3048,3132,3144,3288,3336,3344
%N A325812 Numbers k such that gcd(A034448(k)-k, k-A048146(k)) is equal to abs(k-A048146(k)).
%C A325812 Numbers k for which A325813(k) is equal to abs(A325814(k)).
%C A325812 Numbers k such that A325814(k) is not zero (not in A064591) and divides A034460(k).
%C A325812 Conjecture: after the initial one all other terms are even. If this holds then there are no odd perfect numbers.
%H A325812 Antti Karttunen, <a href="/A325812/b325812.txt">Table of n, a(n) for n = 1..25000</a>
%H A325812 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%o A325812 (PARI)
%o A325812 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A325812 A034460(n) = (A034448(n) - n);
%o A325812 A048146(n) = (sigma(n)-A034448(n));
%o A325812 A325814(n) = (n-A048146(n));
%o A325812 A325813(n) = gcd(A034460(n), A325814(n));
%o A325812 isA325812(n) = (A325813(n)==abs(A325814(n)));
%o A325812 \\ Alternatively:
%o A325812 isA325812(n) = (A325814(n) && !(A034460(n)%A325814(n)));
%Y A325812 Cf. A034448, A034460, A048146, A064591, A325813, A325814, A325822.
%Y A325812 Cf. A000396 (a subsequence).
%K A325812 nonn
%O A325812 1,2
%A A325812 _Antti Karttunen_, May 23 2019