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

1,2

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

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: {{},{},{},{},{},{}}

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A331913 A318612 A318690 * A243497 A214577 A280994

Adjacent sequences: A302495 A302496 A302497 * A302499 A302500 A302501

Keyword

nonn

Author

Gus Wiseman, Apr 09 2018

Status

approved