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A355370
Irregular triangle read by rows in which row n lists the numbers that divide the sum of the digits of their n-th powers.
1
1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 9, 1, 2, 3, 8, 9, 17, 18, 26, 27, 1, 3, 6, 7, 9, 22, 25, 28, 36, 1, 3, 9, 28, 35, 36, 46, 1, 2, 3, 7, 9, 18, 23, 45, 54, 64, 1, 3, 6, 9, 12, 15, 18, 27, 31, 34, 43, 53, 58, 68, 1, 3, 5, 6, 9, 15, 27, 46, 54, 63
OFFSET
0,3
COMMENTS
For the proof of finiteness of rows, see comments in A309017.
It appears that the right column is A046000.
EXAMPLE
Triangle begins:
n=0: 1;
n=1: 1, 2, 3, 4, 5, 6, 7, 8, 9;
n=2: 1, 2, 3, 9;
n=3: 1, 2, 3, 8, 9, 17, 18, 26, 27;
n=4: 1, 3, 6, 7, 9, 22, 25, 28, 36;
n=5: 1, 3, 9, 28, 35, 36, 46;
n=6: 1, 2, 3, 7, 9, 18, 23, 45, 54, 64;
n=7: 1, 3, 6, 9, 12, 15, 18, 27, 31, 34, 43, 53, 58, 68;
n=8: 1, 3, 5, 6, 9, 15, 27, 46, 54, 63;
n=9: 1, 2, 3, 6, 7, 9, 16, 27, 36, 54, 71, 81;
n=10: 1, 3, 5, 6, 9, 18, 36, 82, 85, 94, 97, 106, 117;
...
PROG
(Python)
def ok(k, n): return sum(map(int, str(k**n)))%k==0
def row(n):
d, lim = 1, 1
while lim < n*9*d: d, lim = d+1, lim*10
yield from [k for k in range(1, lim+1) if ok(k, n)]
print([an for n in range(9) for an in row(n)]) # Michael S. Branicky, Jul 06 2022
CROSSREFS
Row lengths are A355563.
Sequence in context: A349194 A342829 A247796 * A326344 A340270 A115026
KEYWORD
tabf,nonn,base
AUTHOR
Mohammed Yaseen, Jun 30 2022
STATUS
approved