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

1,2

Comments

The prime numbers in A068807 belong to the sequence.

Links

Table of n, a(n) for n=1..56.

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A318206 A385575 A022442 * A056689 A034037 A330331

Adjacent sequences: A308160 A308161 A308162 * A308164 A308165 A308166

Keyword

nonn,base

Author

Marius A. Burtea, Jun 11 2019

Status

approved