A302498 Numbers that are a power of a prime number whose prime index is itself a power of a prime number.

1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 23, 25, 27, 31, 32, 41, 49, 53, 59, 64, 67, 81, 83, 97, 103, 109, 121, 125, 127, 128, 131, 157, 179, 191, 211, 227, 241, 243, 256, 277, 283, 289, 311, 331, 343, 353, 361, 367, 401, 419, 431, 461, 509, 512, 529, 547, 563

Offset: 1

Author

Gus Wiseman, Apr 09 2018

Keywords

• nonn

Comments

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

Examples

			49 is in the sequence because 49 = prime(prime(1)^2)^2.
Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of constant constant-multiset multisystems.
01: {}
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
07: {{1,1}}
08: {{},{},{}}
09: {{1},{1}}
11: {{3}}
16: {{},{},{},{}}
17: {{4}}
19: {{1,1,1}}
23: {{2,2}}
25: {{2},{2}}
27: {{1},{1},{1}}
31: {{5}}
32: {{},{},{},{},{}}
41: {{6}}
49: {{1,1},{1,1}}
53: {{1,1,1,1}}
59: {{7}}
64: {{},{},{},{},{},{}}
		

Links

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

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A076610, A275024, A279789, A295920, A301763, A302242, A302243, A302492, A302493, A302496, A302497.

Programs

Mathematica

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

PARI

ok(n)={my(p); n == 1 || (isprimepower(n, &p) && (p == 2 || isprimepower(primepi(p))))} \\ Andrew Howroyd, Aug 26 2018