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%I #34 Mar 31 2023 06:29:03
%S 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,
%T 29,31,32,33,34,35,37,38,39,41,42,43,44,46,47,49,50,51,52,53,54,55,57,
%U 58,59,61,62,64,65,66,67,68,69,71,73,74,75,76,77,78,79,81,82,83,85,86,87
%N 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.
%C 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
%H Ivan Neretin, <a href="/A027855/b027855.txt">Table of n, a(n) for n = 1..10000</a>
%p 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:
%p for n from 2 to 120 do if isA027855(n) then printf("%d, ",n) ; fi ; od: # _R. J. Mathar_, Dec 02 2007
%t Select[Range@100, #1^(#2 + 1) & @@ FactorInteger[#][[-1]] > # &] (* _Ivan Neretin_, Jul 09 2015 *)
%o (Python)
%o from sympy import factorint, primefactors
%o def a053585(n):
%o if n==1: return 1
%o p = primefactors(n)[-1]
%o return p**factorint(n)[p]
%o print([n for n in range(2, 301) if n//a053585(n)<primefactors(n)[-1]]) # _Indranil Ghosh_, Jul 13 2017
%o (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
%Y Cf. A006530, A027854, A051119.
%K nonn
%O 1,1
%A _Leroy Quet_
%E More terms from _R. J. Mathar_, Dec 02 2007
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