A138311 a(1)=1. a(n) = smallest positive integer not occurring among the first n-1 terms of the sequence that is coprime to every (nonzero) exponent in the prime factorization of n.

1, 2, 3, 5, 4, 6, 7, 8, 9, 10, 11, 13, 12, 14, 15, 17, 16, 19, 18, 21, 20, 22, 23, 25, 27, 24, 26, 29, 28, 30, 31, 32, 33, 34, 35, 37, 36, 38, 39, 40, 41, 42, 43, 45, 47, 44, 46, 49, 51, 53, 48, 55, 50, 52, 54, 56, 57, 58, 59, 61, 60, 62, 63, 65, 64, 66, 67, 69, 68, 70, 71, 73

Offset

1,2

Links

Diana Mecum, Table of n, a(n) for n = 1..1000

Example

12 has the prime-factorization of 2^2 * 3^1. The positive integers that don't occur among the first 11 terms of the sequence are 12,13,14,15,16,... Of these integers, 13 is the smallest that is coprime to the exponents in the prime factorization of 12 (i.e., coprime to 2 and 1). So a(12) = 13.

Mathematica

With[{nn = 72}, Fold[Append[#1, SelectFirst[Range[2, 2 nn], Function[k, And[FreeQ[#1, k], AllTrue[FactorInteger[#2][[All, -1]], CoprimeQ[k, #] &]]]]] &, {1}, Range[2, nn]]] (* Michael De Vlieger, Oct 18 2017 *)

Crossrefs

Cf. A138309, A138310.

Sequence in context: A262564 A222240 A309151 * A131717 A084489 A084490

Adjacent sequences: A138308 A138309 A138310 * A138312 A138313 A138314

Keyword

nonn

Author

Leroy Quet, Mar 13 2008

Extensions

More terms from Diana L. Mecum, Jul 21 2008

Status

approved