A109659 Numbers k such that the sum of the digits of sigma(k)^k is divisible by k.

1, 15, 20, 34, 42, 44, 50, 101, 107, 558, 584, 750, 1491, 2793, 2889, 15811, 27285, 60030, 67258, 87066

Offset

1,2

Comments

Next term after 2889, if it exists, is greater than 10000.

Next term, if it exists, is greater than 30000. - Sean A. Irvine, Feb 24 2010

Next term, if it exists, is greater than 100000. - Michael S. Branicky, Jan 27 2023

Links

Table of n, a(n) for n=1..20.

Example

The digits of sigma(1491)^1491 sum to 22365 and 22365 is divisible by 1491, so 1491 is in the sequence.

Mathematica

Do[s = DivisorSigma[1, n]^n; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]

Prog

(Python)
from sympy import divisor_sigma
def ok(n): return n and (sum(map(int, str(divisor_sigma(n, 1)**n)))%n == 0)
print([k for k in range(3000) if ok(k)]) # Michael S. Branicky, Jan 27 2023

Crossrefs

Sequence in context: A086770 A111200 A088494 * A294149 A065148 A093028

Adjacent sequences: A109656 A109657 A109658 * A109660 A109661 A109662

Keyword

base,more,nonn

Author

Ryan Propper, Aug 06 2005

Extensions

a(16)-a(17) from Sean A. Irvine, Feb 24 2010

a(18)-a(20) from Michael S. Branicky, Jan 27 2023

Status

approved