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%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
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