A380447 Odd numbers k for which A339792(k), the third coefficient of the lindep transform of sigma, is 0.

1, 585, 819, 1989, 2295, 3515, 4095, 4455, 4655, 5733, 6201, 6435, 7155, 9009, 10251, 10545, 11115, 13923, 13965, 14725, 15147, 16965, 18837, 23751, 28665, 31635, 32205, 33579, 34485, 34515, 36309, 38745, 41895, 43407, 45045, 46359, 46781, 47223, 49005, 51319, 52065, 53955, 55341, 58149, 60515, 62015, 63063, 63855

Offset

1,2

Comments

Odd numbers k for which A000203(k)*A339790(k) = -k*A339791(k).

First squares in this sequence are: 1, 480249, 2140369, 3538161, ..., see A380449 and A380450.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Example

585 is included as sigma(585)*A339790(585) = -585*A339791(585), i.e., 1092*15 = -585 * -28 = 16380.
480249 is included as sigma(480249)*A339790(480249) = -480249*A339791(480249), i.e., 917301*189 = -480249 * -361 = 173369889.

Prog

(PARI)
A339792(n) = { my(v=lindep([sigma(n), n, 1])); (v*sign(v[1]))[3]; };
A380445(n) = !A339792(n);
is_A380447(n) = ((n%2) && A380445(n));

Crossrefs

Odd terms in A380446.

Cf. A000203, A339790, A339791, A339792, A380445, A380449 (squares in this sequence), A380450 (their square roots).

Sequence in context: A205069 A187050 A252195 * A037995 A250627 A043428

Adjacent sequences: A380444 A380445 A380446 * A380448 A380449 A380450

Keyword

nonn

Author

Antti Karttunen, Jan 25 2025

Status

approved