A083792 Lexicographically first increasing sequence such that no two successive terms have the same prime signature.

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

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(n-1) while s(k)=s(a(n-1)) 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