A245303 - OEIS

%I #33 Aug 13 2014 22:17:16

%S 2,3,5,7,8,11,12,13,16,17,18,19,20,23,24,27,28,29,31,32,37,40,41,43,

%T 44,45,47,48,50,52,53,54,56,59,61,63,64,67,68,71,72,73,75,76,79,80,81,

%U 83,88,89,92,96,97,98,99,101,103,104,107,108,109,112,113,116,117,124,125,127,128,131

%N Product of a prime and a power (exponent at least 2, base at least 1).

%C Numbers of the form p*m^r where p prime, m > 0 and r > 1.

%H Jens Kruse Andersen, <a href="/A245303/b245303.txt">Table of n, a(n) for n = 1..10000</a>

%e 72 is in this sequence because 72 = 2*36 = A000040(1)*A001597(9).

%e 108 is in this sequence because 108 = 3*36 = A000040(2)*A001597(9).

%p filter:= proc(n) local E,ne,i,j;

%p   if isprime(n) then return true fi;

%p   E:= map(t->t[2],ifactors(n)[2]);

%p   ne:= nops(E);

%p   for j from 1 to ne do

%p      if igcd(seq(`if`(i=j,E[i]-1,E[i]),i=1..ne)) > 1 then return true fi;

%p   od;

%p   false

%p end proc:

%p filter(1):= false:

%p select(filter, [$1..1000]); # _Robert Israel_, Aug 11 2014

%o (PARI) ispp(n) = (n==1) || ispower(n);

%o isok(n) = {my(f = factor(n)); for (i=1, #f~, p = f[i, 1]; if (ispp(n/p), return(1));); return (0);} \\ _Michel Marcus_, Aug 08 2014

%Y Cf. A000040, A001597, A245661.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jul 17 2014