

A027854


Mutinous 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.


8



12, 24, 30, 36, 40, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 108, 112, 120, 126, 132, 135, 140, 144, 150, 154, 160, 165, 168, 175, 176, 180, 182, 189, 192, 195, 198, 200, 208, 210, 216, 220, 224, 225, 231, 234, 240, 252, 260, 264, 270, 273, 275, 280
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OFFSET

1,1


COMMENTS

Numbers n > 1 such that n/A053585(n) > A006530(n).  Michael De Vlieger, Jul 13 2017
If p = A006530(a(n)) then p * a(n) is in the sequence. E.g. As 12 is in the sequence with Gpf(12) = A006530(12) = 3, 12*3^k is in the sequence for k > 0. Conjecture: if m is in the sequence then so is A003961(m).  David A. Corneth, Jul 13 2017
At present this and A027855 are complements in the set of integers >= 2. If a 1 were inserted at the start, then this and A027855 are complements in the set of positive integers.  Harry Richman, Sep 08 2019


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000


EXAMPLE

From Michael De Vlieger, Jul 13 2017: (Start)
12 is a term since 12/A053585(12) = 12/3 = 4, A006530(12) = 3, and 4 > 3.
30 is a term since 30/A053585(30) = 30/5 = 6, A006530(30) = 5, and 6 > 5.
(End)


MATHEMATICA

Select[Range@ 280, Function[n, (n/Apply[Power, Last@ #]) > #[[1, 1]] &@ FactorInteger[n]]] (* Michael De Vlieger, Jul 13 2017 *)


PROG

(PARI) isok(n) = {my(f = factor(n)); my(maxf = #f~); my(p = f[maxf, 1]); my(pk = f[maxf, 2]); (n/p^pk) > p; } \\ Michel Marcus, Jan 16 2014
(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


CROSSREFS

Cf. A006530, A027855, A053585.
Sequence in context: A074697 A333919 A289484 * A009096 A010814 A334760
Adjacent sequences: A027851 A027852 A027853 * A027855 A027856 A027857


KEYWORD

nonn


AUTHOR

Leroy Quet.


EXTENSIONS

Extended by Ray Chandler, Nov 17 2008
Offset changed to 1 by Michel Marcus, Jan 16 2014


STATUS

approved



