A141567 Bases and exponents in the prime decomposition of n replaced by nonprimes with these indices.

0, 1, 4, 1, 8, 4, 10, 1, 4, 8, 16, 4, 20, 10, 32, 1, 25, 4, 27, 8, 40, 16, 33, 4, 8, 20, 256, 10, 40, 32, 44, 1, 64, 25, 80, 4, 51, 27, 80, 8, 56, 40, 58, 16, 32, 33, 64, 4, 10, 8, 100, 20, 72, 256, 128, 10, 108, 40, 80, 32, 82, 44, 40, 1, 160, 64, 90, 25, 132, 80, 94, 4, 96, 51, 32

Offset

1,3

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)=A141468(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..75.

Maple

A141468 := proc(n) option remember ; local a; if n <= 2 then n-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(0) fi; a := 1; for p in ifs do q := A141468(op(1, p)) ; if op(2, p) > 1 then e := A141468(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, A141468.

Sequence in context: A340527 A021709 A193337 * A254707 A134417 A116080

Adjacent sequences: A141564 A141565 A141566 * A141568 A141569 A141570

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 17 2008

Extensions

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

Status

approved