A069492 5-full numbers: if p divides n then so does p^5.

1, 32, 64, 128, 243, 256, 512, 729, 1024, 2048, 2187, 3125, 4096, 6561, 7776, 8192, 15552, 15625, 16384, 16807, 19683, 23328, 31104, 32768, 46656, 59049, 62208, 65536, 69984, 78125, 93312, 100000, 117649, 124416, 131072, 139968, 161051

Offset

1,2

Comments

a(m) mod prime(n) > 0 for m < A258602(n); a(A258602(n)) = A050997(n) = prime(n)^5. - Reinhard Zumkeller, Jun 06 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^4*(p-1))) = 1.0695724994489739263413712783666538355049945684326048537289707764272637... - Amiram Eldar, Jul 09 2020

Prog

(PARI) for(n=1, 250000, if(n*sumdiv(n, d, isprime(d)/d^5)==floor(n*sumdiv(n, d, isprime(d)/d^5)), print1(n, ", ")))
(Haskell)
import Data.Set (singleton, deleteFindMin, fromList, union)
a069492 n = a069492_list !! (n-1)
a069492_list = 1 : f (singleton z) [1, z] zs where
   f s q5s p5s'@(p5:p5s)
     | m < p5 = m : f (union (fromList $ map (* m) ps) s') q5s p5s'
     | otherwise = f (union (fromList $ map (* p5) q5s) s) (p5:q5s) p5s
     where ps = a027748_row m
           (m, s') = deleteFindMin s
   (z:zs) = a050997_list
-- Reinhard Zumkeller, Jun 03 2015

Crossrefs

Cf. A036967, A036966, A001694.

Cf. A050997.

Cf. A258602.

Sequence in context: A255995 A144908 A172419 * A076469 A256819 A358250

Adjacent sequences: A069489 A069490 A069491 * A069493 A069494 A069495

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 15 2002

Status

approved