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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.

%I A129401 #25 Mar 01 2018 08:34:44
%S A129401 9,15,27,25,21,45,33,35,81,75,63,55,39,135,49,51,125,99,105,243,65,57,
%T A129401 77,225,69,85,189,165,117,175,87,405,121,147,95,153,375,91,297,115,93,
%U A129401 315,111,275,729,119,195,171,145,231,675,123,245,207,143,255,567,625
%N A129401 a(n) is the result of replacing with its successor prime each prime in the factorization of the n-th composite number.
%C A129401 Each odd composite number appears in the sequence exactly once. - _Jon E. Schoenfield_, Jun 05 2007
%C A129401 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
%H A129401 Harvey P. Dale, <a href="/A129401/b129401.txt">Table of n, a(n) for n = 1..1000</a>
%F A129401 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]
%F A129401 a(n) = A045965(A002808(n)). - _Ivan N. Ianakiev_, Feb 15 2018
%e A129401 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.
%t A129401 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 *)
%o A129401 (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
%Y A129401 Cf. A002808 (composite numbers), A003961.
%K A129401 nonn
%O A129401 1,1
%A A129401 _Ben Paul Thurston_, May 28 2007
%E A129401 More terms from _Jon E. Schoenfield_, Jun 05 2007
%E A129401 Name edited by _Jon E. Schoenfield_, Feb 18 2018