

A129401


a(n) is the result of replacing with its successor prime each prime in the factorization of the nth composite number.


1



9, 15, 27, 25, 21, 45, 33, 35, 81, 75, 63, 55, 39, 135, 49, 51, 125, 99, 105, 243, 65, 57, 77, 225, 69, 85, 189, 165, 117, 175, 87, 405, 121, 147, 95, 153, 375, 91, 297, 115, 93, 315, 111, 275, 729, 119, 195, 171, 145, 231, 675, 123, 245, 207, 143, 255, 567, 625
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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



FORMULA



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



EXTENSIONS



STATUS

approved



