|
Search: id:A141566
|
|
|
| A141566 |
|
Primes and exponents in the prime number decomposition of n replaced by primes at these positions. |
|
+0
1
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
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, (mathar(AT)strw.leidenuniv.nl), Aug 21 2008
|
|
CROSSREFS
|
Cf. A000040, A002808.
Sequence in context: A068543 A064026 A121264 this_sequence A078736 A042669 A041585
Adjacent sequences: A141563 A141564 A141565 this_sequence A141567 A141568 A141569
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 17 2008
|
|
EXTENSIONS
|
Edited and corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 21 2008
|
|
|
Search completed in 0.002 seconds
|
