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A308163 Numbers for which the sum of the digits of any divisor is a power of 2. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A161607 A318206 A022442 * A056689 A034037 A330331

Adjacent sequences:  A308160 A308161 A308162 * A308164 A308165 A308166

KEYWORD

nonn,base

AUTHOR

Marius A. Burtea, Jun 11 2019

STATUS

approved

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Last modified September 28 19:16 EDT 2021. Contains 347717 sequences. (Running on oeis4.)