A302539 Squarefree numbers whose prime indices other than 1 are prime numbers.

1, 2, 3, 5, 6, 10, 11, 15, 17, 22, 30, 31, 33, 34, 41, 51, 55, 59, 62, 66, 67, 82, 83, 85, 93, 102, 109, 110, 118, 123, 127, 134, 155, 157, 165, 166, 170, 177, 179, 186, 187, 191, 201, 205, 211, 218, 241, 246, 249, 254, 255, 277, 283, 295, 310, 314, 327, 330

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..10000

Formula

Sum_{n>=1} 1/a(n) = (3/2) * Product_{p in A006450} (1 + 1/p) converges since the sum of the reciprocals of A006450 converges. - Amiram Eldar, Feb 02 2021

Example

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}}
05: {{2}}
06: {{},{1}}
10: {{},{2}}
11: {{3}}
15: {{1},{2}}
17: {{4}}
22: {{},{3}}
30: {{},{1},{2}}
31: {{5}}
33: {{1},{3}}
34: {{},{4}}
41: {{6}}
51: {{1},{4}}
55: {{2},{3}}
59: {{7}}
62: {{},{5}}
66: {{},{1},{3}}

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[400], SquareFreeQ[#]&&And@@(PrimeQ/@DeleteCases[primeMS[#], 1])&]

Prog

(PARI) ok(n)={issquarefree(n) && !#select(p->p>2 && !isprime(primepi(p)), factor(n)[, 1])} \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A281113, A302242, A302243, A302534.

Sequence in context: A255059 A057760 A074243 * A322912 A072720 A325354

Adjacent sequences: A302536 A302537 A302538 * A302540 A302541 A302542

Keyword

nonn

Author

Gus Wiseman, Apr 09 2018

Status

approved