cp's OEIS Frontend

A320325 Numbers whose product of prime indices is a perfect power.

%I A320325 #6 Oct 11 2018 10:10:03
%S A320325 7,9,14,18,19,21,23,25,27,28,36,38,42,46,49,50,53,54,56,57,63,72,76,
%T A320325 81,84,92,97,98,100,103,106,108,112,114,115,121,125,126,131,133,144,
%U A320325 147,151,152,159,161,162,168,169,171,175,183,184,185,189,194,195,196
%N A320325 Numbers whose product of prime indices is a perfect power.
%C A320325 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 A320325 The terms together with their corresponding multiset multisystems (A302242):
%e A320325    7: {{1,1}}
%e A320325    9: {{1},{1}}
%e A320325   14: {{},{1,1}}
%e A320325   18: {{},{1},{1}}
%e A320325   19: {{1,1,1}}
%e A320325   21: {{1},{1,1}}
%e A320325   23: {{2,2}}
%e A320325   25: {{2},{2}}
%e A320325   27: {{1},{1},{1}}
%e A320325   28: {{},{},{1,1}}
%e A320325   36: {{},{},{1},{1}}
%e A320325   38: {{},{1,1,1}}
%e A320325   42: {{},{1},{1,1}}
%e A320325   46: {{},{2,2}}
%e A320325   49: {{1,1},{1,1}}
%e A320325   50: {{},{2},{2}}
%e A320325   53: {{1,1,1,1}}
%e A320325   54: {{},{1},{1},{1}}
%e A320325   56: {{},{},{},{1,1}}
%e A320325   57: {{1},{1,1,1}}
%e A320325   63: {{1},{1},{1,1}}
%e A320325   72: {{},{},{},{1},{1}}
%e A320325   76: {{},{},{1,1,1}}
%e A320325   81: {{1},{1},{1},{1}}
%t A320325 Select[Range[100],GCD@@FactorInteger[Times@@Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]^k]][[All,2]]>1&]
%Y A320325 Cf. A000720, A001222, A001597, A003963, A056239, A064573, A112798, A302242, A305551, A306017, A319056, A319066, A320322, A320323, A320324.
%K A320325 nonn
%O A320325 1,1
%A A320325 _Gus Wiseman_, Oct 10 2018