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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.
3
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
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
Sequence in context: A262564 A222240 A309151 * A131717 A084489 A084490
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 13 2008
EXTENSIONS
More terms from Diana L. Mecum, Jul 21 2008
STATUS
approved