cp's OEIS Frontend

A302492 Products of any power of 2 with prime numbers of prime-power index, i.e., prime numbers p of the form p = prime(q^k), for q prime, k >= 1.

%I A302492 #12 Aug 27 2018 01:53:02
%S A302492 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,27,28,
%T A302492 30,31,32,33,34,35,36,38,40,41,42,44,45,46,48,49,50,51,53,54,55,56,57,
%U A302492 59,60,62,63,64,66,67,68,69,70,72,75,76,77,80,81,82,83
%N A302492 Products of any power of 2 with prime numbers of prime-power index, i.e., prime numbers p of the form p = prime(q^k), for q prime, k >= 1.
%C A302492 A prime index of n is a number m such that prime(m) divides n.
%H A302492 Andrew Howroyd, <a href="/A302492/b302492.txt">Table of n, a(n) for n = 1..1000</a>
%e A302492 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset multisystems.
%e A302492 01: {}
%e A302492 02: {{}}
%e A302492 03: {{1}}
%e A302492 04: {{},{}}
%e A302492 05: {{2}}
%e A302492 06: {{},{1}}
%e A302492 07: {{1,1}}
%e A302492 08: {{},{},{}}
%e A302492 09: {{1},{1}}
%e A302492 10: {{},{2}}
%e A302492 11: {{3}}
%e A302492 12: {{},{},{1}}
%e A302492 14: {{},{1,1}}
%e A302492 15: {{1},{2}}
%e A302492 16: {{},{},{},{}}
%e A302492 17: {{4}}
%e A302492 18: {{},{1},{1}}
%e A302492 19: {{1,1,1}}
%e A302492 20: {{},{},{2}}
%e A302492 21: {{1},{1,1}}
%e A302492 22: {{},{3}}
%e A302492 23: {{2,2}}
%e A302492 24: {{},{},{},{1}}
%t A302492 Select[Range[100],Or[#===1,And@@PrimePowerQ/@PrimePi/@DeleteCases[FactorInteger[#][[All,1]],2]]&]
%o A302492 (PARI) ok(n)={!#select(p->p<>2&&!isprimepower(primepi(p)), factor(n)[,1])} \\ _Andrew Howroyd_, Aug 26 2018
%Y A302492 Cf. A000961, A001222, A003963, A005117, A007716, A050361, A056239, A076610, A270995, A275024, A279784, A281113, A295935, A301762, A302242, A302243, A302493.
%K A302492 nonn
%O A302492 1,2
%A A302492 _Gus Wiseman_, Apr 08 2018