A392925 Smallest odd number k greater than 1 such that sigma_n(k)/k is an integer.

65, 3913, 5617, 1717, 65, 145, 6069, 135, 65, 3417, 5617, 1431, 65, 231, 2350089, 10131, 65, 98045, 5617, 145, 65, 134667, 32079, 1717, 65, 135, 5617, 22633, 65, 6341, 2350089, 483, 65, 145, 5617, 224321, 65, 1113, 4097, 475839, 65, 7745, 5617, 135, 65, 10345

Offset

2,1

Comments

a(1) corresponds to odd multiperfect numbers greater than 1, if they exist.

Does every integer greater than 1 have a solution?

65 is a solution for every positive n congruent to 2 mod 4.

Links

Alexander Violette, Table of n, a(n) for n = 2..200

Wikipedia, Divisor function

Example

65 is the smallest odd number k > 1 such that sigma_2(k)/k is an integer, hence a(2)=65.

Prog

(PARI) a(n) = my(k=3); while (sigma(k, n) % k, k+=2); k; \\ Michel Marcus, May 30 2026

Crossrefs

Cf. A000203, A066135 (even), A007691 (mpn).

Sequence in context: A069225 A211960 A293695 * A133853 A188693 A206876

Adjacent sequences: A392922 A392923 A392924 * A392926 A392927 A392928

Keyword

nonn

Author

Alexander Violette, May 13 2026

Status

approved