A224488 Numbers m such that k*m = Sum_{j|m, j < m} sigma(j), where k >= 1 is an integer.

4, 10, 42, 90, 2448, 4680, 27144, 117000, 154498509, 222970077, 11049088050, 63554826816

Offset: 1

Author

Giovanni Resta, Apr 08 2013

Keywords

• nonn
• more

Comments

a(13) > 10^11.

Examples

			The divisors of 10 smaller than 10 are 1, 2 and 5. Since sigma(1) + sigma(2) + sigma(5) = 10, 10 is in the sequence.
		

Crossrefs

Cf. A211779, A221219.

Programs

Mathematica

Select[Range[2, 120000], Mod[Total@DivisorSigma[1, Most@Divisors@#], #] == 0 &]

PARI

isok(m) = sumdiv(m, d, if (d!=m, sigma(d))) % m == 0; \\ Michel Marcus, Jul 13 2021

Extensions

a(9)-a(12) and bound on a(13) from Donovan Johnson.