A356061 Numbers whose sum of digits is a refactorable number.

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.

Links

Table of n, a(n) for n=1..63.

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

Cf. A000005, A033950, A007953, A306509, A356520.

Sequence in context: A152754 A001560 A175463 * A167450 A050569 A352698

Adjacent sequences: A356058 A356059 A356060 * A356062 A356063 A356064

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Aug 10 2022

Status

approved