A302601 Numbers that are powers of a prime number whose prime index is also a prime power (not including 1).

1, 3, 5, 7, 9, 11, 17, 19, 23, 25, 27, 31, 41, 49, 53, 59, 67, 81, 83, 97, 103, 109, 121, 125, 127, 131, 157, 179, 191, 211, 227, 241, 243, 277, 283, 289, 311, 331, 343, 353, 361, 367, 401, 419, 431, 461, 509, 529, 547, 563, 587, 599, 617, 625, 661, 691, 709

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

49 is in the sequence because 49 = prime(4)^2 = 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 multiset multisystems.
001: {}
003: {{1}}
005: {{2}}
007: {{1,1}}
009: {{1},{1}}
011: {{3}}
017: {{4}}
019: {{1,1,1}}
023: {{2,2}}
025: {{2},{2}}
027: {{1},{1},{1}}
031: {{5}}
041: {{6}}
049: {{1,1},{1,1}}
053: {{1,1,1,1}}
059: {{7}}
067: {{8}}
081: {{1},{1},{1},{1}}
083: {{9}}
097: {{3,3}}
103: {{2,2,2}}
109: {{10}}
121: {{3},{3}}
125: {{2},{2},{2}}
127: {{11}}
131: {{1,1,1,1,1}}

Mathematica

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

Prog

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

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243, A302498.

Sequence in context: A342949 A322400 A322553 * A064076 A050842 A143447

Adjacent sequences: A302598 A302599 A302600 * A302602 A302603 A302604

Keyword

nonn

Author

Gus Wiseman, Apr 10 2018

Status

approved