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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.

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