A069493 6-full numbers: if p divides n then so does p^6.

1, 64, 128, 256, 512, 729, 1024, 2048, 2187, 4096, 6561, 8192, 15625, 16384, 19683, 32768, 46656, 59049, 65536, 78125, 93312, 117649, 131072, 139968, 177147, 186624, 262144, 279936, 373248, 390625, 419904, 524288, 531441, 559872, 746496, 823543, 839808

Offset

1,2

Comments

a(m) mod prime(n) > 0 for m < A258603(n); a(A258600(n)) = A030516(n) = prime(n)^6. - Reinhard Zumkeller, Jun 06 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^5*(p-1))) = 1.0334657852594050612296726462481884631303137561267151463866539131591664... - Amiram Eldar, Jul 09 2020

Example

2^7*3^6 = 93312 is a member (although not of A076470).

Mathematica

Join[{1}, Select[Range[900000], Min[FactorInteger[#][[All, 2]]]>5&]] (* Harvey P. Dale, Mar 03 2018 *)

Prog

(PARI) for(n=1, 560000, if(n*sumdiv(n, d, isprime(d)/d^6)==floor(n*sumdiv(n, d, isprime(d)/d^6)), print1(n, ", ")))
(Haskell)
import Data.Set (singleton, deleteFindMin, fromList, union)
a069493 n = a069493_list !! (n-1)
a069493_list = 1 : f (singleton z) [1, z] zs where
   f s q6s p6s'@(p6:p6s)
     | m < p6 = m : f (union (fromList $ map (* m) ps) s') q6s p6s'
     | otherwise = f (union (fromList $ map (* p6) q6s) s) (p6:q6s) p6s
     where ps = a027748_row m
           (m, s') = deleteFindMin s
   (z:zs) = a030516_list
-- Reinhard Zumkeller, Jun 03 2015

Crossrefs

Cf. A036967, A036966, A001694. Different from A076470.

Cf. A030516, A258603.

Sequence in context: A043335 A023708 A172420 * A076470 A256820 A031464

Adjacent sequences: A069490 A069491 A069492 * A069494 A069495 A069496

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 15 2002

Status

approved