A325812 - OEIS

%I #16 Jun 18 2019 16:12:35

%S 1,6,12,28,56,60,108,120,132,168,264,280,312,408,420,440,456,496,528,

%T 540,552,696,700,728,744,756,760,888,984,992,1032,1128,1140,1188,1272,

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

%C Numbers k for which A325813(k) is equal to abs(A325814(k)).

%C Numbers k such that A325814(k) is not zero (not in A064591) and divides A034460(k).

%C Conjecture: after the initial one all other terms are even. If this holds then there are no odd perfect numbers.

%H Antti Karttunen, <a href="/A325812/b325812.txt">Table of n, a(n) for n = 1..25000</a>

%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 A325813(n) = gcd(A034460(n), A325814(n));

%o isA325812(n) = (A325813(n)==abs(A325814(n)));

%o \\ Alternatively:

%o isA325812(n) = (A325814(n) && !(A034460(n)%A325814(n)));

%Y Cf. A034448, A034460, A048146, A064591, A325813, A325814, A325822.

%Y Cf. A000396 (a subsequence).

%K nonn

%O 1,2

%A _Antti Karttunen_, May 23 2019