A073919 Smallest prime p with bigomega(p-1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity).

2, 3, 5, 13, 17, 73, 97, 193, 257, 769, 3457, 7681, 15361, 12289, 40961, 114689, 65537, 737281, 1376257, 786433, 5308417, 7340033, 14155777, 28311553, 104857601, 113246209, 167772161, 469762049, 2113929217, 1811939329

Offset: 0

Author

Amarnath Murthy, Aug 18 2002

Keywords

• nonn

Examples

			a(2) = 5 = 2*2 + 1. a(5) = 73 = 2*2*2*3*3 + 1.
		

Links

• David W. Wilson and Robert G. Wilson v, Table of n, a(n) for n = 0..351

Crossrefs

Cf. A118883.

Programs

Mathematica

ptns[n_, 0] := If[n==0, {{}}, {}]; ptns[n_, k_] := Module[{r}, If[nv, Return[v]]; minp=Min@@Select[l+1, ProvablePrimeQ]; If[minpHarvey P. Dale, Sep 28 2014 *)

PARI

almost_primes(A, B, n) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p, ceil(A/m)), B\m, listput(list, m*q)), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 2, n)));
a(n) = if(n==0, return(2)); my(x=2^n, y=2*x); while(1, my(v=almost_primes(x, y, n)); for(k=1, #v, if(isprime(v[k]+1), return(v[k]+1))); x=y+1; y=2*x); \\ Daniel Suteu, Jan 07 2025

Extensions

Edited by Dean Hickerson, Nov 12 2002