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A308163
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Numbers for which the sum of the digits of any divisor is a power of 2.
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0
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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
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OFFSET
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1,2
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COMMENTS
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The prime numbers in A068807 belong to the sequence.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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