A287932 a(n) = least k > n such that lpf(n) = lpf(k), where lpf = least prime factor (A020639).

4, 9, 6, 25, 8, 49, 10, 15, 12, 121, 14, 169, 16, 21, 18, 289, 20, 361, 22, 27, 24, 529, 26, 35, 28, 33, 30, 841, 32, 961, 34, 39, 36, 55, 38, 1369, 40, 45, 42, 1681, 44, 1849, 46, 51, 48, 2209, 50, 77, 52, 57, 54, 2809, 56, 65, 58, 63, 60, 3481, 62, 3721, 64

Offset

2,1

Comments

This sequence is a permutation of the composite numbers (A002808).

a(p) = p^2 for any prime p (see A001248).

a(2*k) = 2*k + 2 for any k > 1.

For any prime p and n >= 0, a^n(p)/p is the (n+1)-th p-rough number (where a^n denotes the n-th iterate of a).

See also A071830 for the largest prime factor equivalent.

Links

Rémy Sigrist, Table of n, a(n) for n = 2..10000

Mathematica

lpf[n_] := FactorInteger[n][[1, 1]]; a[n_] := Block[{k, p = lpf[n]}, k=n+p; While[lpf[k] != p, k += p]; k]; Array[a, 61, 2] (* Giovanni Resta, Jun 04 2017 *)

Prog

(PARI) a(n) = my (l=factor(n)[1, 1]); forstep (v=n+l, oo, l, if (factor(v)[1, 1]==l, return (v)))

Crossrefs

Cf. A002808, A020639, A071830.

A001248 is a subsequence.

Sequence in context: A362436 A140694 A152454 * A074767 A016097 A083717

Adjacent sequences: A287929 A287930 A287931 * A287933 A287934 A287935

Keyword

nonn

Author

Rémy Sigrist, Jun 03 2017

Status

approved