A027855 Antimutinous numbers: n>1 such that n/p^k < p, where p is the largest prime dividing n and p^k is the highest power of p dividing n.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87

Offset

1,1

Comments

Numbers which can be expressed as m*p^k, for p prime and m < p and k > 0. List contains n if A006530(n) > A051119(n). - Harry Richman, Aug 19 2019

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Maple

isA027855 := proc(n) local p, k, pk; if n <= 1 then false; else p := A006530(n) ; pk := p ; while n mod ( pk*p) = 0 do pk := pk*p ; od: if n< p*pk then true ; else false ; fi ; fi ; end proc:
for n from 2 to 120 do if isA027855(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Dec 02 2007

Mathematica

Select[Range@100, #1^(#2 + 1) & @@ FactorInteger[#][[-1]] > # &] (* Ivan Neretin, Jul 09 2015 *)

Prog

(Python)
from sympy import factorint, primefactors
def a053585(n):
    if n==1: return 1
    p = primefactors(n)[-1]
    return p**factorint(n)[p]
print([n for n in range(2, 301) if n//a053585(n)<primefactors(n)[-1]]) # Indranil Ghosh, Jul 13 2017
(PARI) is(n) = my(f = factor(n)); c = n\f[#f~, 1]^f[#f~, 2]; c < f[#f~, 1] \\ David A. Corneth, Aug 19 2019

Crossrefs

Cf. A006530, A027854, A051119.

Sequence in context: A299702 A348577 A361232 * A031996 A023753 A035332

Adjacent sequences: A027852 A027853 A027854 * A027856 A027857 A027858

Keyword

nonn

Author

Leroy Quet

Extensions

More terms from R. J. Mathar, Dec 02 2007

Status

approved