A320325 - OEIS

%I #6 Oct 11 2018 10:10:03

%S 7,9,14,18,19,21,23,25,27,28,36,38,42,46,49,50,53,54,56,57,63,72,76,

%T 81,84,92,97,98,100,103,106,108,112,114,115,121,125,126,131,133,144,

%U 147,151,152,159,161,162,168,169,171,175,183,184,185,189,194,195,196

%N Numbers whose product of prime indices is a perfect power.

%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

%e The terms together with their corresponding multiset multisystems (A302242):

%e    7: {{1,1}}

%e    9: {{1},{1}}

%e   14: {{},{1,1}}

%e   18: {{},{1},{1}}

%e   19: {{1,1,1}}

%e   21: {{1},{1,1}}

%e   23: {{2,2}}

%e   25: {{2},{2}}

%e   27: {{1},{1},{1}}

%e   28: {{},{},{1,1}}

%e   36: {{},{},{1},{1}}

%e   38: {{},{1,1,1}}

%e   42: {{},{1},{1,1}}

%e   46: {{},{2,2}}

%e   49: {{1,1},{1,1}}

%e   50: {{},{2},{2}}

%e   53: {{1,1,1,1}}

%e   54: {{},{1},{1},{1}}

%e   56: {{},{},{},{1,1}}

%e   57: {{1},{1,1,1}}

%e   63: {{1},{1},{1,1}}

%e   72: {{},{},{},{1},{1}}

%e   76: {{},{},{1,1,1}}

%e   81: {{1},{1},{1},{1}}

%t Select[Range[100],GCD@@FactorInteger[Times@@Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]^k]][[All,2]]>1&]

%Y Cf. A000720, A001222, A001597, A003963, A056239, A064573, A112798, A302242, A305551, A306017, A319056, A319066, A320322, A320323, A320324.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 10 2018