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A027855
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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.
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4
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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
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graph;
refs;
listen;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Ivan Neretin, Table of n, a(n) for n = 1..10000
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MAPLE
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A006530 := proc(n) local ifs ; if n = 1 then 1; else ifs := ifactors(n)[2] ; max(seq( op(1, k), k=ifs)) ; fi ; end: 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: for n from 2 to 120 do if isA027855(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Dec 02 2007
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MATHEMATICA
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Select[Range@100, #1^(#2 + 1) & @@ FactorInteger[#][[-1]] > # &] (* Ivan Neretin, Jul 09 2015 *)
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PROG
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(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
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CROSSREFS
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Cf. A006530, A027854, A051119.
Sequence in context: A325778 A299702 A348577 * A031996 A023753 A035332
Adjacent sequences: A027852 A027853 A027854 * A027856 A027857 A027858
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet
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EXTENSIONS
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More terms from R. J. Mathar, Dec 02 2007
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STATUS
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approved
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