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A129401
a(n) is the result of replacing with its successor prime each prime in the factorization of the n-th 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
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
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]
a(n) = A045965(A002808(n)). - Ivan N. Ianakiev, Feb 15 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
Cf. A002808 (composite numbers), A003961.
Sequence in context: A333788 A082549 A013569 * A164385 A339519 A258813
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