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A134193
a(1) = 1; for n>1, a(n) = the smallest positive integer not occurring among the exponents in the prime-factorization of n.
5
1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 1, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 1, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 3, 3, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 1, 2, 2, 2, 2, 2, 2
OFFSET
1,2
FORMULA
a(n) = A257993(A181819(n)). - Antti Karttunen, Jul 28 2017
EXAMPLE
The prime factorization of 24 is 2^3 * 3^1. The exponents are 3 and 1. Therefore a(24) = 2 is the smallest positive integer not occurring among (3,1).
MATHEMATICA
Table[Complement[Range[n], Table[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}]][[1]], {n, 2, 120}] (* Stefan Steinerberger, Jan 21 2008 *)
PROG
(Scheme) (define (A134193 n) (A257993 (A181819 n))) ;; Antti Karttunen, Jul 28 2017
(PARI) a(n) = if (n==1, 1, my(f=factor(n)); ve = vecsort(f[, 2], , 8); k = 1; while(vecsearch(ve, k), k++); k; ); \\ Michel Marcus, Jul 28 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jan 13 2008
EXTENSIONS
More terms from Stefan Steinerberger, Jan 21 2008
STATUS
approved