A302592 One, powers of 2, and prime numbers of prime index.

1, 2, 3, 4, 5, 8, 11, 16, 17, 31, 32, 41, 59, 64, 67, 83, 109, 127, 128, 157, 179, 191, 211, 241, 256, 277, 283, 331, 353, 367, 401, 431, 461, 509, 512, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1024, 1031, 1063, 1087, 1153, 1171

Offset

1,2

Links

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

Formula

Union of A000079 and A006450. - Andrew Howroyd, Aug 26 2018

Example

Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
001: {}
002: {{}}
003: {{1}}
004: {{},{}}
005: {{2}}
008: {{},{},{}}
011: {{3}}
016: {{},{},{},{}}
017: {{4}}
031: {{5}}
032: {{},{},{},{},{}}
041: {{6}}
059: {{7}}
064: {{},{},{},{},{},{}}
067: {{8}}
083: {{9}}
109: {{10}}
127: {{11}}
128: {{},{},{},{},{},{},{}}

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Or[#===1, Union[primeMS[#]]==={1}, PrimeQ[#]&&PrimeQ[PrimePi[#]]]&]

Prog

(PARI) ok(n)={n>>valuation(n, 2) == 1 || (isprime(n) && isprime(primepi(n)))} \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A279791, A281113, A296133, A301765, A302242, A302243.

Sequence in context: A244395 A271488 A333347 * A078762 A103262 A135318

Adjacent sequences: A302589 A302590 A302591 * A302593 A302594 A302595

Keyword

nonn

Author

Gus Wiseman, Apr 10 2018

Status

approved