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A356061
Numbers whose sum of digits is a refactorable number.
1
1, 2, 8, 9, 10, 11, 17, 18, 20, 26, 27, 35, 36, 39, 44, 45, 48, 53, 54, 57, 62, 63, 66, 71, 72, 75, 80, 81, 84, 90, 93, 99, 100, 101, 107, 108, 110, 116, 117, 125, 126, 129, 134, 135, 138, 143, 144, 147, 152, 153, 156, 161, 162, 165, 170, 171, 174, 180, 183, 189, 192, 198, 200
OFFSET
1,2
COMMENTS
Also numbers k such that A007953(k) = c * A000005(A007953(k)); c >= 1 is a positive integer. For c = 1 see A356520.
EXAMPLE
k = 17; A007953(17) = 2 * A000005(A007953(17)), thus k = 17 is in the sequence.
MAPLE
filter:= proc(n) local s; s:= convert(convert(n, base, 10), `+`); s mod numtheory:-tau(s) = 0 end proc:
select(filter, [$1..200]); # Robert Israel, Aug 10 2022
MATHEMATICA
refQ[n_] := Divisible[n, DivisorSigma[0, n]]; Select[Range[2000], refQ[Plus @@ IntegerDigits[#]] &] (* Amiram Eldar, Aug 10 2022 *)
PROG
(Python)
from sympy import divisor_count
def ok(n): sd = sum(map(int, str(n))); return sd%divisor_count(sd) == 0
print([k for k in range(1, 200) if ok(k)]) # Michael S. Branicky, Aug 10 2022
(PARI) isok(k) = my(s=sumdigits(k)); denominator(s/numdiv(s)) == 1; \\ Michel Marcus, Aug 10 2022
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Ctibor O. Zizka, Aug 10 2022
STATUS
approved