A110878 Positive integers k such that the sum of the divisors of k, excluding 1, is a multiple of the number of divisors of k.

1, 2, 4, 9, 16, 25, 36, 64, 81, 100, 121, 289, 400, 529, 625, 729, 841, 1024, 1089, 1296, 1681, 2025, 2116, 2209, 2304, 2401, 2809, 3025, 3481, 4096, 5041, 6724, 6889, 7569, 7921, 10201, 11449, 12769, 13456, 13924, 15625, 17161, 18769, 19881

Offset

1,2

Comments

It appears that all terms except the second are squares. This has been verified for all terms less than one million.

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

The 9 divisors of 36 are {1,2,3,4,6,9,12,18,36}, giving sigma(36)-1=90, which is a multiple of 9. Thus 36 is a term of the sequence.

Mathematica

Select[Range[20000], Divisible[DivisorSigma[1, #]-1, DivisorSigma[0, #]]&] (* Harvey P. Dale, Dec 23 2020 *)

Crossrefs

Sequence in context: A015730 A073858 A006474 * A253849 A364131 A077137

Adjacent sequences: A110875 A110876 A110877 * A110879 A110880 A110881

Keyword

nonn

Author

John W. Layman, Sep 19 2005

Status

approved