A308163 Numbers for which the sum of the digits of any divisor is a power of 2.

1, 2, 4, 8, 11, 13, 17, 22, 26, 31, 44, 53, 62, 71, 79, 88, 97, 101, 103, 107, 121, 143, 169, 187, 202, 206, 211, 233, 242, 251, 277, 286, 341, 349, 367, 404, 422, 431, 439, 457, 466, 484, 503, 521, 547, 583, 619, 673, 682, 691, 701, 709, 727, 781, 808, 844

Offset: 1

Author

Marius A. Burtea, Jun 11 2019

Keywords

• nonn
• base

Comments

The prime numbers in A068807 belong to the sequence.

Examples

			Divisors(8) = {1, 2, 4, 8} with sums of digits respectively 1, 2, 4, 8, powers of 2.
Divisors(13) = {1, 13} with sums of digits 1 and 4, powers of 2 .
Divisors(286) = {1, 2, 11, 13, 22, 26, 143, 286} with sums of digits respectively 1, 2, 2, 4, 4, 8, 16, powers of 2.
		

Crossrefs

Cf. A000005, A000079, A007953, A068807, A028838.

Programs

Magma

sol:=[]; m:=1;for n in [1..850] do nr:=#[d: d in Divisors(n) | PrimeDivisors(&+Intseq(d)) eq [2]];  if nr eq #Divisors(n)-1 then sol[m]:=n; m:=m+1; end if; end for; sol;

PARI

ispp(n) = (n==1) || (isprimepower(n, &p) && (p==2));
isok(n) = fordiv(n, d, if (!ispp(sumdigits(d)), return (0))); return (1); \\ Michel Marcus, Jun 12 2019