A261564 a(1)=2; thereafter a(n) = mpf(1+Product_{k=1..n-1} a(k)), where mpf(n) = f-th prime factor with multiplicity of n, for f=ceiling(bigomega(n)/2).

2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 25621, 10300271, 2731, 1079927141307582051252331702244209088763871

Offset: 1

Author

Anders Hellström, Aug 24 2015

Keywords

• nonn
• more

Links

• Anders Hellström, Ruby program

Crossrefs

Cf. A079879, A001222, A000945, A000946.

Programs

Mathematica

f[n_] := Block[{p = Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n], len}, len = Length@ p; Which[n == 1, 1, OddQ@len, p[[1 + Floor[len/2]]], True, p[[len/2]]]]; a = {2}; Do[AppendTo[a, f[1 + Product[a[[k]], {k, 1, n - 1}]]], {n, 2, 13}] ; a (* Michael De Vlieger, Aug 25 2015 *)

PARI

factorsm(n)=my(v=factor(n), f=factor(n)[, 1]~, w=[]); for(i=1, #f, for(j=1, v[i, 2], w=concat(w, f[i]))); w;
mpf(n)=my(f=factorsm(n)); f[ceil(#f/2)]
first(m)=my(v=vector(m)); v[1]=2; for(i=2, m, v[i]=mpf(1+prod(j=1, i-1, v[j]))); v;

Formula

a(1)=2; thereafter a(n) = A079879(1+Product_{k=1..n-1}a(k)).

Extensions

a(13) from Michael De Vlieger, Aug 25 2015