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

Author

Ilya Gutkovskiy, Jan 01 2017

Keywords

• nonn
• easy

Comments

Intersection of A020487 and A033950.

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of divisors

Crossrefs

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

Programs

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 *)