OFFSET
1,1
COMMENTS
Each odd composite number appears in the sequence exactly once. - Jon E. Schoenfield, Jun 05 2007
Prime factors are used with multiplicity, e.g., the factors of 4 are 2 and 2, and both terms are replaced by 3, so a(1) = 3*3 = 9. - Harvey P. Dale, Mar 19 2013
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = A003961(A002808(n)). - Jon E. Schoenfield, Jun 04 2007 [edited, at the suggestion of Michel Marcus, by Jon E. Schoenfield, Feb 18 2018]
EXAMPLE
a(19) = 105 because the factorization of the 19th composite number (i.e., 30) is 2*3*5 and replacing each prime factor with the next prime results in 3*5*7 which remultiplies to 105.
MATHEMATICA
cnp[n_]:=Times@@(NextPrime/@Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[ n]]); With[{nn=100}, cnp/@Complement[Range[2, nn], Prime[Range[PrimePi[nn]]]]] (* Harvey P. Dale, Mar 19 2013 *)
PROG
(PARI) lista(nn) = {forcomposite(c=1, nn, my (f = factor(c)); for (k=1, #f~, f[k, 1] = nextprime(f[k, 1]+1)); print1(factorback(f), ", "); ); } \\ Michel Marcus, Feb 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ben Paul Thurston, May 28 2007
EXTENSIONS
More terms from Jon E. Schoenfield, Jun 05 2007
Name edited by Jon E. Schoenfield, Feb 18 2018
STATUS
approved