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

Author

Ben Paul Thurston, May 28 2007

Keywords

• nonn

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

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002808 (composite numbers), A003961.

Programs

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 *)

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

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

Extensions

More terms from Jon E. Schoenfield, Jun 05 2007

Name edited by Jon E. Schoenfield, Feb 18 2018