A302540 Numbers whose prime indices other than 1 are prime numbers.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 17, 18, 20, 22, 24, 25, 27, 30, 31, 32, 33, 34, 36, 40, 41, 44, 45, 48, 50, 51, 54, 55, 59, 60, 62, 64, 66, 67, 68, 72, 75, 80, 81, 82, 83, 85, 88, 90, 93, 96, 99, 100, 102, 108, 109, 110, 118, 120, 121, 123, 124

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

Formula

Sum_{n>=1} 1/a(n) = 2 * Sum_{n>=1} 1/A076610(n) = 2 * Product_{p in A006450} p/(p-1) converges since the sum of the reciprocals of A006450 converges. - Amiram Eldar, Feb 02 2021

Mathematica

Select[Range[400], #===1||And@@(#===1||PrimeQ[#]&)/@PrimePi/@FactorInteger[#][[All, 1]]&]

Prog

(PARI) ok(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, A291686, A302242, A302243, A302534, A302539.

Sequence in context: A269164 A356899 A230780 * A332487 A067942 A130176

Adjacent sequences: A302537 A302538 A302539 * A302541 A302542 A302543

Keyword

nonn

Author

Gus Wiseman, Apr 09 2018

Status

approved