A302591 One, powers of 2, and prime numbers of squarefree index.

1, 2, 3, 4, 5, 8, 11, 13, 16, 17, 29, 31, 32, 41, 43, 47, 59, 64, 67, 73, 79, 83, 101, 109, 113, 127, 128, 137, 139, 149, 157, 163, 167, 179, 181, 191, 199, 211, 233, 241, 256, 257, 269, 271, 277, 283, 293, 313, 317, 331, 347, 349, 353, 367, 373, 389, 397, 401

Offset: 1

Author

Gus Wiseman, Apr 10 2018

Keywords

• nonn

Comments

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

Examples

			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: {{},{},{}}
11: {{3}}
13: {{1,2}}
16: {{},{},{},{}}
17: {{4}}
29: {{1,3}}
31: {{5}}
32: {{},{},{},{},{}}
41: {{6}}
43: {{1,4}}
47: {{2,3}}
59: {{7}}
64: {{},{},{},{},{},{}}
		

Links

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

Crossrefs

Cf. A000079, A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279791, A281113, A296133, A301765, A302242, A302243, A302491.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[400],Or[#===1,Union[primeMS[#]]==={1},PrimeQ[#]&&SquareFreeQ[PrimePi[#]]]&]

PARI

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

Formula

Union of A000079 and A302491. - Andrew Howroyd, Aug 26 2018