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.

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, 30, 31, 32, 33, 34, 35, 36, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 68, 69, 70, 72, 75, 76, 77, 80, 81, 82, 83

Offset: 1

Author

Gus Wiseman, Apr 08 2018

Keywords

• nonn

Comments

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

Examples

			Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset multisystems.
01: {}
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
06: {{},{1}}
07: {{1,1}}
08: {{},{},{}}
09: {{1},{1}}
10: {{},{2}}
11: {{3}}
12: {{},{},{1}}
14: {{},{1,1}}
15: {{1},{2}}
16: {{},{},{},{}}
17: {{4}}
18: {{},{1},{1}}
19: {{1,1,1}}
20: {{},{},{2}}
21: {{1},{1,1}}
22: {{},{3}}
23: {{2,2}}
24: {{},{},{},{1}}
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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

PARI

ok(n)={!#select(p->p<>2&&!isprimepower(primepi(p)), factor(n)[,1])} \\ Andrew Howroyd, Aug 26 2018