A129401 a(n) is the result of replacing with its successor prime each prime in the factorization of the n-th composite number.

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

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]

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

Adjacent sequences: A129398 A129399 A129400 * A129402 A129403 A129404

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