A141568 Bases and exponents in the prime decomposition of n replaced by nonprimes with these indices.

1, 4, 6, 256, 9, 24, 12, 4096, 1296, 36, 18, 1536, 21, 48, 54, 65536, 26, 5184, 28, 2304, 72, 72, 34, 24576, 6561, 84, 46656, 3072, 42, 216, 45, 262144, 108, 104, 108, 331776, 52, 112, 126, 36864, 57, 288, 60, 4608, 11664, 136, 65, 393216, 20736, 26244, 156

Offset

1,2

Comments

Start from the prime decomposition of n, not writing down exponents which equal 1; that is the list 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3,.. Replace each number i in this representation by the nonprime r(i)=A018252(i). This generates the sequence of a(n), namely r(1), r(2), r(3), r(2)^r(2), r(5), r(2)*r(3), r(7), r(2)^r(3), r(3)^r(2), r(2)*r(5), r(11), r(2)^r(2)*r(3),...

Links

Table of n, a(n) for n=1..51.

Maple

A018252 := proc(n) option remember ; local a; if n = 1 then 1 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: A := proc(n) local a, p, e, q, ifs ; ifs := ifactors(n)[2] ; if n = 1 then RETURN(1) fi; a := 1; for p in ifs do q := A018252(op(1, p)) ; if op(2, p) > 1 then e := A018252(op(2, p)) ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 120 do printf("%d, ", A(n)) ; od: # R. J. Mathar, Aug 21 2008

Crossrefs

Cf. A000040, A002808, A018252.

Sequence in context: A298147 A081970 A076098 * A113838 A056831 A027717

Adjacent sequences: A141565 A141566 A141567 * A141569 A141570 A141571

Keyword

nonn,mult

Author

Juri-Stepan Gerasimov, Aug 17 2008

Extensions

Edited and corrected by R. J. Mathar, Aug 21 2008

Status

approved