A141566 Primes and exponents in the prime number decomposition of n replaced by primes at these positions.

2, 3, 5, 27, 11, 15, 17, 243, 125, 33, 31, 135, 41, 51, 55, 2187, 59, 375, 67, 297, 85, 93, 83, 1215, 1331, 123, 3125, 459, 109, 165, 127, 177147, 155, 177, 187, 3375, 157, 201, 205, 2673, 179, 255, 191, 837, 1375, 249, 211, 10935, 4913, 3993, 295, 1107, 241

Offset

1,1

Comments

Start from the prime decomposition of n, 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 visible number (in the sense that exponents which equal 1 are invisible and not written down) by the prime number which carries that index. This gives the sequence of a(n), namely p(1), p(2), p(3), p(2)^p(2), p(5), p(2)*p(3), p(7), p(2)^p(3), p(3)^p(2), p(2)*p(5), p(11), p(2)^p(2)*p(3),..), where p=A000040 are the primes.

Links

Table of n, a(n) for n=1..53.

Maple

A := proc(n) local a, p, e, q, ifs ; ifs := ifactors(n)[2] ; if n = 1 then RETURN(2) fi; a := 1; for p in ifs do q := ithprime(op(1, p)) ; if op(2, p) > 1 then e := ithprime(op(2, p)) ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 80 do printf("%d, ", A(n)) ; od: # R. J. Mathar, Aug 21 2008

Crossrefs

Cf. A000040, A002808.

Sequence in context: A068543 A064026 A121264 * A247094 A078736 A042669

Adjacent sequences: A141563 A141564 A141565 * A141567 A141568 A141569

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 17 2008

Extensions

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

Status

approved