A135975 -id:A135975 - cp's OEIS frontend

A135386 Mersenne composites A065341 with 4 or more prime factors.

10384593717069655257060992658440191, 2854495385411919762116571938898990272765493247, 182687704666362864775460604089535377456991567871

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..102

Subsequence of A065341.

Cf. A000225, A054723, A134852, A135975, A135976, A135977, A135979.

A135386 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (nops(numtheory[factorset](i)) > 3) then
   RETURN (i)
fi: end: seq(A135386(n), n=1..37); # Jani Melik, Feb 09 2011

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; If[d >3, AppendTo[k, 2^Prime[n] - 1]]], {n, 1, 40}]; k

A319908 Lesser of twin primes pair p, such that the Mersenne numbers 2^p - 1 and 2^(p+2) - 1 have the same number of prime factors.

Original entry on oeis.org

3, 5, 17, 71, 101, 137, 197, 269, 617, 857, 1019, 1049, 1061

Offset: 1

Amiram Eldar, Oct 01 2018

The corresponding number of prime factors is 1, 1, 1, 3, 2, 2, 2, 2, 4, 4, 5, 4, 2, ...

Assuming that Mersenne numbers (2^p-1 with p prime) are always squarefree, the distinction between number of prime factors with multiplicity (A001222) and number of different prime factors (A001221) is inessential.

			3 is in the sequence since 3 and 5 are twin primes pair, and 2^3-1=7 and 2^5-1=31 are both primes, thus having the same number of prime factors.
71 is in the sequence since 71 and 73 are twin primes pair and 2^71-1 and 2^73-1 both have 3 prime factors.

Cf. A000225, A001359, A065341, A135975.

Do[If[PrimeQ[n]&&PrimeQ[n+2]&&PrimeOmega[2^n-1]==PrimeOmega[2^(n+2)-1],Print[n]],{n,1,200}]

isok(p) = isprime(p) && isprime(p+2) && (omega(2^p-1) == omega(2^(p+2)-1)); \\ Michel Marcus, Oct 02 2018

cp's OEIS Frontend

A135386 Mersenne composites A065341 with 4 or more prime factors.

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