A136033 -id:A136033 - cp's OEIS frontend

A140745 Smallest prime p such that the Mersenne number A000225(p) = 2^p - 1 has exactly n prime factors (counted with multiplicity).

2, 11, 29, 157, 113, 223, 491, 431, 397

Offset: 1

Lekraj Beedassy, Jul 12 2008

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 223, pp 63-4, Ellipse Paris 2008.

a[n_]:=Module[{p=0},Until[PrimeOmega[2^Prime[p]-1]==n,p++];Prime[p]];Array[a,6] (* James C. McMahon, Jul 14 2025 *)

a(n) = forprime(p=2, oo, if(bigomega(2^p-1)==n, return(p))); \\ Jinyuan Wang, Aug 10 2021

A136034 a(n) = smallest number k such that number of distinct prime factors of 2^k-1 is exactly n.

Original entry on oeis.org

1, 2, 4, 8, 12, 20, 24, 40, 36, 48, 88, 60, 72, 150, 132, 120, 156, 144, 200, 204, 210, 180, 324, 476, 288, 300, 432, 396, 480, 360, 468, 576, 700, 504, 420, 648, 540, 660, 792, 720

Offset: 0

Artur Jasinski, Dec 11 2007

First occurrence of n in A046800.

Cf. A000225, A003260, A016047, A046051, A046800, A049479, A088863, A136030, A136031, A136032, A136033.

With[{pn1=PrimeNu[2^Range[800]-1]},Table[Position[pn1,n,1,1],{n,0,40}]]//Flatten (* Harvey P. Dale, Jan 10 2025 *)

a(n) = my(k=1); while (omega(2^k-1) != n, k++); k; \\ Michel Marcus, Jan 09 2023

More terms from Julián Aguirre, Feb 04 2013
a(31)-a(39) from Chai Wah Wu, Oct 03 2019
a(0) = 1 inserted by Michel Marcus, Jan 09 2023

cp's OEIS Frontend

A140745 Smallest prime p such that the Mersenne number A000225(p) = 2^p - 1 has exactly n prime factors (counted with multiplicity).

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