A280353 Numbers n such that the sum of the divisors of n divides sum of squares of divisors of n and number of divisors of n divides n.

1, 9, 36, 180, 225, 441, 450, 468, 625, 1089, 1476, 1521, 1620, 1800, 2025, 2178, 2340, 2601, 3249, 3600, 4050, 4500, 4761, 5202, 5625, 6561, 7569, 8100, 8649, 8712, 9522, 10000, 12321, 13572, 15129, 15138, 16200, 16641, 19881, 20808, 22500, 23400, 25281, 26244, 28224, 28800

Offset

1,2

Comments

Intersection of A020487 and A033950.

Numbers n such that A000203(n)|A001157(n) and A000005(n)|n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of divisors

Example

9 is in the sequence because 9 has 3 divisors {1,3,9}, 9/3 = 3 and (1^2 + 3^2 + 9^2)/(1 + 3 + 9) = 7 are both integer.

Mathematica

Select[Range[30000], Divisible[DivisorSigma[2, #1], DivisorSigma[1, #1]] && Divisible[#1, DivisorSigma[0, #1]] & ]
Select[Range[30000], With[{ds=DivisorSigma}, Mod[ds[2, #], ds[1, #]]==Mod[#, ds[0, #]]==0&]] (* Harvey P. Dale, Nov 27 2024 *)

Crossrefs

Cf. A000005, A000203, A001157, A020487, A033950.

Sequence in context: A245416 A265837 A264359 * A110752 A094973 A038780

Adjacent sequences: A280350 A280351 A280352 * A280354 A280355 A280356

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Jan 01 2017

Status

approved