A135979 -id:A135979 - cp's OEIS frontend

A135977 Mersenne composites (A065341) with exactly 3 prime factors.

536870911, 8796093022207, 140737488355327, 9007199254740991, 2361183241434822606847, 9444732965739290427391, 604462909807314587353087

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..42

Subsequence of A065341.

Cf. A000225, A054723, A134852, A135975, A135976, A135978, A135979, A344515.

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

a(n) = 2^A344515(n) - 1. - Amiram Eldar, May 23 2021

A135976 Mersenne composites (A065341) with exactly 2 prime factors.

Original entry on oeis.org

2047, 8388607, 137438953471, 2199023255551, 576460752303423487, 147573952589676412927, 9671406556917033397649407, 158456325028528675187087900671, 2535301200456458802993406410751

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..39
Wikipedia, Semiprime.

Subsequence of A065341.

Cf. A000225, A054723, A134852, A135975, A135977, A135978, A135979.

A135976 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (nops(numtheory[factorset](i)) = 2) then
   RETURN (i)
fi: end: [ seq(A135976(n), n=1..26) ]; # Jani Melik, Feb 09 2011

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

forprime(p=1, 1e2, if(bigomega(2^p-1)==2, print1(2^p-1, ", "))) \\ Felix Fröhlich, Aug 12 2014

a(n) = 2^A135978(n) - 1. - Amiram Eldar, May 23 2021

A135980 Numbers k such that the Mersenne number 2^prime(k)-1 is composite.

Original entry on oeis.org

5, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

A135979 is a subsequence of this sequence.

Cf. A000225, A065341, A054723, A134852, A135975, A135976, A135977, A135978, A135979.

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], AppendTo[k, n]], {n, 1, 40}]; k
m = PrimePi @ MersennePrimeExponent @ Range[13]; Complement[Range[m[[-1]]], m] (* Amiram Eldar, Mar 12 2020 *)

isok(k) = !isprime(2^prime(k)-1); \\ Michel Marcus, Mar 12 2020

prime(a(n)) = A054723(n).

a(n) = pi(A054723(n)).

More terms from Amiram Eldar, Mar 12 2020

A135386 Mersenne composites A065341 with 4 or more prime factors.

Original entry on oeis.org

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

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A135977 Mersenne composites (A065341) with exactly 3 prime factors.

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A135976 Mersenne composites (A065341) with exactly 2 prime factors.

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A135980 Numbers k such that the Mersenne number 2^prime(k)-1 is composite.

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A135386 Mersenne composites A065341 with 4 or more prime factors.

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