A302492 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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}}

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A023806 A113763 A322847 * A023754 A371968 A335467

Adjacent sequences: A302489 A302490 A302491 * A302493 A302494 A302495

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 08 2018

STATUS

approved