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

9, 12, 27, 16, 18, 36, 24, 24, 81, 48, 54, 32, 36, 108, 36, 42, 64, 72, 72, 243, 48, 54, 48, 144, 60, 56, 162, 96, 108, 96, 72, 324, 64, 108, 72, 126, 192, 72, 216, 80, 90, 216, 96, 128, 729, 84, 144, 162, 96, 144, 432, 114, 144, 180, 96, 168, 486, 256

Offset: 1

Author

Ben Paul Thurston, May 06 2007

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A003959, A249140.

Programs

Maple

b:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 3, b(n-1))
      while isprime(k) do od; k
    end:
a:= n-> mul((i[1]+1)^i[2], i=ifactors(b(n))[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 23 2014

Mathematica

f[n_] := Module[{p, e},
     Product[{p, e} = pe; (p+1)^e, {pe, FactorInteger[n]}]];
f /@ Select[Range[1000], CompositeQ] (* Jean-François Alcover, Jul 11 2021 *)

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

Formula

a(n) = A003959(A002808(n)). - Michel Marcus, Oct 22 2014

Extensions

More terms from Michel Marcus, Jun 26 2013