A043772 Numbers k such that all divisors of k are lucky numbers.

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

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