A302492 - OEIS

%I #12 Aug 27 2018 01:53:02

%S 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 30,31,32,33,34,35,36,38,40,41,42,44,45,46,48,49,50,51,53,54,55,56,57,

%U 59,60,62,63,64,66,67,68,69,70,72,75,76,77,80,81,82,83

%N 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 A prime index of n is a number m such that prime(m) divides n.

%H Andrew Howroyd, <a href="/A302492/b302492.txt">Table of n, a(n) for n = 1..1000</a>

%e Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset multisystems.

%e 01: {}

%e 02: {{}}

%e 03: {{1}}

%e 04: {{},{}}

%e 05: {{2}}

%e 06: {{},{1}}

%e 07: {{1,1}}

%e 08: {{},{},{}}

%e 09: {{1},{1}}

%e 10: {{},{2}}

%e 11: {{3}}

%e 12: {{},{},{1}}

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

%e 15: {{1},{2}}

%e 16: {{},{},{},{}}

%e 17: {{4}}

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

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

%e 20: {{},{},{2}}

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

%e 22: {{},{3}}

%e 23: {{2,2}}

%e 24: {{},{},{},{1}}

%t Select[Range[100],Or[#===1,And@@PrimePowerQ/@PrimePi/@DeleteCases[FactorInteger[#][[All,1]],2]]&]

%o (PARI) ok(n)={!#select(p->p<>2&&!isprimepower(primepi(p)), factor(n)[,1])} \\ _Andrew Howroyd_, Aug 26 2018

%Y Cf. A000961, A001222, A003963, A005117, A007716, A050361, A056239, A076610, A270995, A275024, A279784, A281113, A295935, A301762, A302242, A302243, A302493.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 08 2018