login
A109659
Numbers k such that the sum of the digits of sigma(k)^k is divisible by k.
0
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
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
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