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A043772 Numbers k such that all divisors of k are lucky numbers. 3
1, 3, 7, 9, 13, 21, 31, 37, 43, 49, 63, 67, 73, 79, 93, 111, 127, 129, 151, 163, 169, 193, 201, 211, 219, 223, 237, 241, 259, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 489, 511, 541, 553, 559, 577, 579, 601, 613, 619, 631, 643, 673, 723, 727, 739, 769 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

21 is included because its (positive) divisors, i.e., 1, 3, 7 and 21, are all lucky numbers.

MAPLE

N:= 10^3: # to get all terms <= N

L:= [seq(2*i+1, i=0..floor((N-1)/2))]:

for n from 2 while n < nops(L) do

  r:= L[n];

  L:= subsop(seq(r*i=NULL, i=1..nops(L)/r), L);

od:

LS:= convert(L, set):

select(t -> numtheory:-divisors(t) subset LS, L); # Robert Israel, Jul 20 2015

MATHEMATICA

lst = Range[1, 776, 2]; i = 2; While[ i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; fQ[n_] := Block[{d = Rest@Divisors@n, k = 1, lmt = DivisorSigma[0, n]}, While[k < lmt && MemberQ[lst, d[[k]]], k++ ]; k == lmt]; Select[lst, fQ@# &] (* Robert G. Wilson v, May 12 2006 *)

CROSSREFS

Cf. A000959.

Cf. A118643 (subset).

Sequence in context: A297002 A111250 A118643 * A176553 A109370 A018663

Adjacent sequences:  A043769 A043770 A043771 * A043773 A043774 A043775

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Oct 08 2000

STATUS

approved

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Last modified January 26 11:12 EST 2021. Contains 340438 sequences. (Running on oeis4.)