A302602 Numbers that are powers of a prime number whose prime index is either 1 or also a prime number.

1, 2, 3, 4, 5, 8, 9, 11, 16, 17, 25, 27, 31, 32, 41, 59, 64, 67, 81, 83, 109, 121, 125, 127, 128, 157, 179, 191, 211, 241, 243, 256, 277, 283, 289, 331, 353, 367, 401, 431, 461, 509, 512, 547, 563, 587, 599, 617, 625, 709, 729, 739, 773, 797, 859, 877, 919

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Example

25 is in the sequence because 25 = prime(3)^2 and 3 is a prime number.
Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set systems.
01: {}
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
08: {{},{},{}}
09: {{1},{1}}
11: {{3}}
16: {{},{},{},{}}
17: {{4}}
25: {{2},{2}}
27: {{1},{1},{1}}
31: {{5}}
32: {{},{},{},{},{}}
41: {{6}}
59: {{7}}
64: {{},{},{},{},{},{}}
67: {{8}}
81: {{1},{1},{1},{1}}
83: {{9}}

Mathematica

Select[Range[1000], #===1||MatchQ[FactorInteger[#], {{_?(#===2||PrimeQ[PrimePi[#]]&), _}}]&]

Prog

(PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && ((p==2) || isprime(primepi(p)))); \\ Michel Marcus, Apr 10 2018

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243.

Sequence in context: A044051 A351204 A083132 * A358459 A358377 A242175

Adjacent sequences: A302599 A302600 A302601 * A302603 A302604 A302605

Keyword

nonn

Author

Gus Wiseman, Apr 10 2018

Status

approved