A134852 -id:A134852 - cp's OEIS frontend

A135960 Indices where records occur in A134852.

1, 2, 4, 14, 37, 59, 144, 173

Offset: 1

Artur Jasinski, Dec 08 2007

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135954, A135955, A135956, A135957, A135958, A135959.

a(7)-a(8) from Amiram Eldar, Sep 01 2019 (calculated from the b-file at A134852)

A135975 Number of prime factors (without multiplicity) in Mersenne composites A065341.

Original entry on oeis.org

2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 4, 5, 2, 4, 3, 4, 5, 3, 2, 2, 3, 6, 2, 4, 4, 6, 2, 5, 3, 4, 2, 2, 3, 2, 3, 2, 5, 3, 4, 4, 3, 5, 2, 3, 3, 6, 5, 2, 2, 5, 3, 9, 4, 3, 5, 2, 8, 4, 4, 3, 5, 2, 4, 6, 3, 4, 2, 7, 3, 4, 4, 2, 5, 4, 5, 3, 5, 4, 3, 6, 4, 3, 4, 3, 4, 4

Offset: 1

Artur Jasinski, Dec 09 2007

nonn

Currently the smallest prime exponent p for which 2^p-1 is incompletely factored is p = 1213. - Gord Palameta, Aug 06 2018

Gord Palameta, Table of n, a(n) for n = 1..183
GIMPS, Status of M1213
S. S. Wagstaff, Jr., Main Tables from the Cunningham Project: cofactor of M1213 is C297.

Cf. A000225, A001221, A065341, A054723, A134852.

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; AppendTo[k, d]], {n, 1, 40}]; k
(PrimeNu /@ Select[2^Prime[Range[40]] - 1, ! PrimeQ[#] &]) (* Jean-François Alcover, Aug 13 2014 *)

forprime(p=1, 1e3, if(!ispseudoprime(2^p-1), print1(omega(2^p-1), ", "))) \\ Felix Fröhlich, Aug 12 2014

a(n) = A001221(A065341(n)). - Michel Marcus, Aug 07 2018

a(29)-a(46) from Felix Fröhlich, Aug 12 2014

a(47)-a(100) from Gord Palameta, Aug 07 2018

A135953 (Nonprime Fibonacci numbers with prime indices) that have exactly 2 prime factors.

Original entry on oeis.org

4181, 1346269, 165580141, 53316291173, 956722026041, 2504730781961, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 573147844013817084101, 10284720757613717413913, 26925748508234281076009

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

Conjecture: All numbers in this sequence are products of two sums of two squares, e.g. 4181 = 37*113 = (1^2+6^2)*(7^2+8^2), 1346269 = 557*2417 = (14^2+19^2)*(4^2+49^2).

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

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135954, A135955, A135956, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 2, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k
Select[Fibonacci[Prime[Range[30]]],PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 18 2012 *)

A135957 a(n) = smallest k such that Fibonacci(prime(k)) has exactly n prime factors.

Original entry on oeis.org

1, 2, 8, 12, 25, 50, 96, 73, 164

Offset: 0

Artur Jasinski, Dec 08 2007

A135958 gives prime(k). Cf. A000045, A001605, A050937, A075737, A134787, A134852.

Edited and extended by David Wasserman, Mar 26 2008

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

Original entry on oeis.org

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

A135956 Members of A050937 (nonprime Fibonacci numbers with prime index) with 5 or more distinct prime factors.

Original entry on oeis.org

322615043836854783580186309282650000354271239929, 1476475227036382503281437027911536541406625644706194668152438732346449273, 22334640661774067356412331900038009953045351020683823507202893507476314037053

Offset: 1

Artur Jasinski, Dec 08 2007

Conjecture: all numbers in this sequence are product of 5 or more sum of two squares

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135954, A135955, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; Print[n]; If[c > 4, Print[Fibonacci[Prime[n]]]; AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 100}]; k

A050937 INTERSECT { A051270 UNION A074969 UNION ... } = A050937 MINUS {A135955 UNION A135954 UNION A135953}. - R. J. Mathar, Jun 09 2008

Edited by R. J. Mathar, Jun 09 2008

A135954 Nonprime Fibonacci numbers with prime indices (A050937) that have exactly 3 prime factors.

Original entry on oeis.org

24157817, 44945570212853, 1500520536206896083277, 50095301248058391139327916261, 11463113765491467695340528626429782121, 30010821454963453907530667147829489881, 2211236406303914545699412969744873993387956988653, 103881042195729914708510518382775401680142036775841

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

Conjecture: All numbers in this sequence are products of three sums of two squares.

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135955, A135956, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 3, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k

f(n) = forprime(x=2, n, p=fibonacci(x); if(!isprime(p) && omega(p) == 3, print1(p", "))) \\ Georg Fischer, Feb 15 2025

a(6)-a(8) from Georg Fischer, Feb 15 2025

A135955 (Nonprime Fibonacci numbers with prime indices, A050937) which have exactly 4 prime factors.

Original entry on oeis.org

83621143489848422977, 6161314747715278029583501626149, 289450641941273985495088042104137, 5193981023518027157495786850488117, 66233869353085486281758142155705206899077

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

Conjecture: All numbers in this sequence are products of four sums of two squares.

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135954, A135956, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 4, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k

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

A135978 Primes p such that 2^p-1 has exactly 2 prime factors.

Original entry on oeis.org

11, 23, 37, 41, 59, 67, 83, 97, 101, 103, 109, 131, 137, 139, 149, 167, 197, 199, 227, 241, 269, 271, 281, 293, 347, 373, 379, 421, 457, 487, 523, 727, 809, 881, 971, 983, 997, 1061, 1063

Offset: 1

Artur Jasinski, Dec 09 2007

a(40)>=1277. - Amiram Eldar, Sep 29 2018

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

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

a(17)-a(37) from Arkadiusz Wesolowski, Jan 26 2012

a(38)-a(39) from Amiram Eldar, Sep 29 2018

cp's OEIS Frontend

A135960 Indices where records occur in A134852.

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A135975 Number of prime factors (without multiplicity) in Mersenne composites A065341.

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A135953 (Nonprime Fibonacci numbers with prime indices) that have exactly 2 prime factors.

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A135957 a(n) = smallest k such that Fibonacci(prime(k)) has exactly n prime factors.

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

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A135956 Members of A050937 (nonprime Fibonacci numbers with prime index) with 5 or more distinct prime factors.

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A135954 Nonprime Fibonacci numbers with prime indices (A050937) that have exactly 3 prime factors.

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Mathematica

PARI

Extensions

A135955 (Nonprime Fibonacci numbers with prime indices, A050937) which have exactly 4 prime factors.

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Mathematica

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

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