A316476 Stable numbers. Numbers whose distinct prime indices are pairwise indivisible.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 64, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 113, 119, 121, 123, 125, 127, 128, 131, 135, 137

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

Index entries for sequences related to prime indices in the factorization of n

Example

The prime indices of 45 are {2,2,3}, so the distinct prime indices are {2,3}, which are pairwise indivisible, so 45 belongs to the sequence.
The prime indices of 105 are {2,3,4}, which are not pairwise indivisible (2 divides 4), so 105 does not belong to the sequence.

Mathematica

Select[Range[100], Select[Tuples[If[#===1, {}, Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]]], 2], UnsameQ@@#&&Divisible@@#&]=={}&]

Prog

(PARI) ok(n)={my(v=apply(primepi, factor(n)[, 1])); for(j=2, #v, for(i=1, j-1, if(v[j]%v[i]==0, return(0)))); 1} \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A056239, A112798, A285572, A285573, A303362, A304713, A316468, A316475, A327393, A327394, A378442 (characteristic function).

Sequence in context: A343857 A257144 A328674 * A056867 A320324 A321698

Adjacent sequences: A316473 A316474 A316475 * A316477 A316478 A316479

Keyword

nonn

Author

Gus Wiseman, Jul 04 2018

Status

approved