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

1, 6, 12, 28, 56, 60, 108, 120, 132, 168, 264, 280, 312, 408, 420, 440, 456, 496, 528, 540, 552, 696, 700, 728, 744, 756, 760, 888, 984, 992, 1032, 1128, 1140, 1188, 1272, 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

Offset: 1

Author

Antti Karttunen, May 23 2019

Keywords

• nonn

Comments

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

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000
• Index entries for sequences where any odd perfect numbers must occur

Crossrefs

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

Cf. A000396 (a subsequence).

Programs

PARI

A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A034460(n) = (A034448(n) - n);
A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));
A325813(n) = gcd(A034460(n), A325814(n));
isA325812(n) = (A325813(n)==abs(A325814(n)));
\\ Alternatively:
isA325812(n) = (A325814(n) && !(A034460(n)%A325814(n)));