

A083792


Lexicographically first increasing sequence such that no two successive terms have the same prime signature.


2



1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81
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OFFSET

1,2


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000


EXAMPLE

From Jon E. Schoenfield, Aug 13 2017: (Start)
a(1) = 1 (which has no prime factors);
a(2) = 2 (a prime);
a(3) cannot be 3, because 2 and 3 have the same prime signature (each is a prime); however, the prime signature of 4 (the square of a prime) differs from that of 2, so a(3) = 4. (End)


MAPLE

s:= n> sort(map(i> i[2], ifactors(n)[2])):
a:= proc(n) option remember; local k; for k from
1+a(n1) while s(k)=s(a(n1)) do od; k
end: a(1):=1:
seq(a(n), n=1..80); # Alois P. Heinz, Mar 09 2018


MATHEMATICA

{1, 2} ~Join~ Select[Range[2, 80], Last /@ FactorInteger[#] != Last /@ FactorInteger[#  1] &] (* Giovanni Resta, Aug 14 2017 *)


CROSSREFS

Cf. A083793.
Sequence in context: A094798 A326178 A162880 * A083794 A133016 A026503
Adjacent sequences: A083789 A083790 A083791 * A083793 A083794 A083795


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, May 07 2003


EXTENSIONS

More terms from James A. Sellers, May 19 2003
Incorrect term 76 removed by Alois P. Heinz, Mar 09 2018


STATUS

approved



