A355563 a(n) is the number of numbers that divide the sum of the digits of their n-th powers.

1, 9, 4, 9, 9, 7, 10, 14, 10, 12, 13, 10, 12, 19, 11, 15, 14, 15, 14, 16, 14, 13, 14, 12, 11, 23, 13, 11, 17, 15, 10, 16, 18, 18, 10, 13, 10, 17, 15, 16, 19, 12, 20, 19, 20, 17, 19, 21, 14, 27, 15, 18, 16, 16, 20, 10, 14, 20, 15, 11, 17, 23, 14, 15, 14, 19, 15

Offset: 0

Author

Mohammed Yaseen, Jul 07 2022

Keywords

• nonn
• base

Comments

Row lengths of A355370.

Crossrefs

Cf. A355370, A046019.

Programs

Python

def ok(k, n): return sum(map(int, str(k**n)))%k==0
def a(n):
    d, lim = 1, 1
    while lim < n*9*d: d, lim = d+1, lim*10
    return sum(1 for k in range(1, lim+1) if ok(k, n))
print([a(n) for n in range(67)]) # Michael S. Branicky, Jul 07 2022