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A114434 To obtain a(n), write the n-th composite number as a product of primes, add 1 to each prime and multiply.

%I A114434 #19 Jul 11 2021 03:45:39
%S A114434 9,12,27,16,18,36,24,24,81,48,54,32,36,108,36,42,64,72,72,243,48,54,
%T A114434 48,144,60,56,162,96,108,96,72,324,64,108,72,126,192,72,216,80,90,216,
%U A114434 96,128,729,84,144,162,96,144,432,114,144,180,96,168,486,256
%N A114434 To obtain a(n), write the n-th composite number as a product of primes, add 1 to each prime and multiply.
%H A114434 Alois P. Heinz, <a href="/A114434/b114434.txt">Table of n, a(n) for n = 1..10000</a>
%F A114434 a(n) = A003959(A002808(n)). - _Michel Marcus_, Oct 22 2014
%p A114434 b:= proc(n) option remember; local k;
%p A114434       for k from 1+`if`(n=1, 3, b(n-1))
%p A114434       while isprime(k) do od; k
%p A114434     end:
%p A114434 a:= n-> mul((i[1]+1)^i[2], i=ifactors(b(n))[2]):
%p A114434 seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 23 2014
%t A114434 f[n_] := Module[{p, e},
%t A114434      Product[{p, e} = pe; (p+1)^e, {pe, FactorInteger[n]}]];
%t A114434 f /@ Select[Range[1000], CompositeQ] (* _Jean-François Alcover_, Jul 11 2021 *)
%o A114434 (PARI) lista(nn) = {forcomposite(c=2, nn, f = factor(c); print1(prod(i=1, #f~, (f[i,1]+1)^f[i,2]), ", "););} \\ _Michel Marcus_, Jun 26 2013
%Y A114434 Cf. A002808, A003959, A249140.
%K A114434 nonn
%O A114434 1,1
%A A114434 _Ben Paul Thurston_, May 06 2007
%E A114434 More terms from _Michel Marcus_, Jun 26 2013