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

1,1

Comments

a(13) > 10^11.

Links

Table of n, a(n) for n=1..12.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A211779, A221219.

Sequence in context: A220817 A346889 A114918 * A149213 A149214 A149215

Adjacent sequences: A224485 A224486 A224487 * A224489 A224490 A224491

Keyword

nonn,more

Author

Giovanni Resta, Apr 08 2013

Extensions

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

Status

approved