OFFSET
1,1
COMMENTS
Starting the sequence at a(1)=1 instead leads to a(n) = n for every positive integer n.
EXAMPLE
12 = 2^2 * 3^1. So the multiset of exponents in the prime factorization of 12 is {1,2}. For a(12), we want the smallest integer > a(11)=53 of the form p^1 * q^2, where p and q are distinct primes. Checking: 54 = 2^1 *3^3, so 54 fails. 55 = 5^1*11^1. 56 = 2^3*7^1. 57 = 3^1*19^1. 58 = 2^1*29^1. 59=59^1. 60 = 2^2*3^1*5^1. 61 = 61^1. 62 = 2^1 *31^1. So 54 through 62 all fail. But 63 = 3^2 * 7^1, which has the same multiset of prime exponents, {1,2}, as 12 has. Therefore a(12) = 63.
MAPLE
pmset := proc(n) local e, a ; a := [] ; for e in ifactors(n)[2] do a := [op(a), e[2]] ; od: sort(a) ; end: A137509 := proc(n) option remember ; local nset, a ; if n = 1 then RETURN(2) ; fi ; nset := pmset(n) ; for a from A137509(n-1)+1 do if pmset(a) = nset then RETURN(a) ; fi ; od: end: seq(A137509(n), n=1..120) ; # R. J. Mathar, May 23 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 23 2008
EXTENSIONS
More terms from R. J. Mathar, May 23 2008
STATUS
approved