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%I #6 Apr 10 2018 21:48:10
%S 1,2,3,5,6,7,10,11,14,15,17,19,21,22,23,30,31,33,34,35,38,41,42,46,51,
%T 53,55,57,59,62,66,67,69,70,77,82,83,85,93,95,97,102,103,105,106,109,
%U 110,114,115,118,119,123,127,131,133,134,138,154,155,157,159
%N Products of distinct primes of prime-power index.
%C A prime index of n is a number m such that prime(m) divides n.
%e Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of constant-multiset systems.
%e 01: {}
%e 02: {{}}
%e 03: {{1}}
%e 05: {{2}}
%e 06: {{},{1}}
%e 07: {{1,1}}
%e 10: {{},{2}}
%e 11: {{3}}
%e 14: {{},{1,1}}
%e 15: {{1},{2}}
%e 17: {{4}}
%e 19: {{1,1,1}}
%e 21: {{1},{1,1}}
%e 22: {{},{3}}
%e 23: {{2,2}}
%e 30: {{},{1},{2}}
%e 31: {{5}}
%e 33: {{1},{3}}
%e 34: {{},{4}}
%e 35: {{2},{1,1}}
%e 38: {{},{1,1,1}}
%t Select[Range[nn],Or[#===1,SquareFreeQ[#]&&And@@PrimePowerQ/@PrimePi/@DeleteCases[FactorInteger[#][[All,1]],2]]&]
%o (PARI) is(n) = if(bigomega(n)!=omega(n), return(0), my(f=factor(n)[, 1]~); for(k=1, #f, if(!isprimepower(primepi(f[k])) && primepi(f[k])!=1, return(0)))); 1 \\ _Felix Fröhlich_, Apr 10 2018
%Y Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279786, A281113, A296131, A301767, A302242, A302243, A302493, A302494.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 09 2018
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