A057600 a(n) is smallest number m such that (m = product of n distinct primes) and all divisors of m are lucky numbers.

3, 21, 777, 61383

Offset

1,1

Comments

a(5) > 2*10^7, if it exists. - Vit Planocka (planocka(AT)mistral.cz), Sep 26 2003

a(5) > 4*10^9, if it exists. - Giovanni Resta, May 10 2020

Links

Table of n, a(n) for n=1..4.

Example

a(2) = 3*7 = 21: divisors of 21 are 1, 3, 7, 21, all of which are lucky numbers.

Mathematica

lst = Range[1, 2*10^7, 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]; t = Table[0, {10}]; Do[ If[ fQ@lst[[n]], a = Length@ FactorInteger@lst[[n]]; If[ t[[a]] == 0, t[[a]] = lst[[n]]; Print[ lst[[n]] ]]], {n, 2, Length@lst}] (* Robert G. Wilson v, May 12 2006 *)

Crossrefs

Cf. A000959.

Sequence in context: A001699 A291967 A171104 * A162924 A079269 A127104

Adjacent sequences: A057597 A057598 A057599 * A057601 A057602 A057603

Keyword

nonn,more

Author

Naohiro Nomoto, Oct 06 2000

Status

approved