

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



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
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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]] & ]


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



