A139306 -id:A139306 - cp's OEIS frontend

A139301 a(n) = (2^(2p - 1)/8)-1, where p is the n-th Mersenne prime A000668(n).

3, 1023, 288230376151711743, 1809251394333065553493296640760748560207343510400633813116524750123642650623

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139302, A139303, A139304, A139305, A139306.

a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 6) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

a(n) = (2^(2*A000668(n)-1)/8)-1 = (A139294(n)/8)-1.

a(4) from Amiram Eldar, Jul 10 2025

A139302 a(n) = 2^(2p - 1)/16, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

2, 512, 144115188075855872, 904625697166532776746648320380374280103671755200316906558262375061821325312

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139303, A139304, A139305, A139306.

a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 7); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

a(n) = 2^(2*A000668(n)-1)/16 = A139294(n)/16.

a(4) from Amiram Eldar, Jul 10 2025

A139303 a(n) = (2^(2p - 1)/16)-1, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

1, 511, 144115188075855871, 904625697166532776746648320380374280103671755200316906558262375061821325311

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139302, A139304, A139305, A139306.

a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 7) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

a(n) = (2^(2*A000668(n)-1)/16)-1 = (A139294(n)/16)-1.

a(4) from Amiram Eldar, Jul 10 2025

A139304 a(n) = 2^(2p - 1)/32, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

1, 256, 72057594037927936, 452312848583266388373324160190187140051835877600158453279131187530910662656

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139302, A139303, A139305, A139306.

a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 8); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

a(n) = 2^(2*A000668(n)-1)/32 = A139294(n)/32.

a(4) from Amiram Eldar, Jul 10 2025

A139305 a(n) = (2^(2p - 1)/32)-1, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

0, 255, 72057594037927935, 452312848583266388373324160190187140051835877600158453279131187530910662655

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Next term is too large to list here.

Cf. A000668, A139286, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139302, A139303, A139304, A139306.

a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 8) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

a(n) = (2^(2*A000668(n)-1)/32)-1 = (A139294(n)/32)-1.

Edited by Max Alekseyev, Apr 23 2010

A139287 2^(2p - 1) - 1, where p is prime.

Original entry on oeis.org

7, 31, 511, 8191, 2097151, 33554431, 8589934591, 137438953471, 35184372088831, 144115188075855871, 2305843009213693951, 9444732965739290427391, 2417851639229258349412351, 38685626227668133590597631

Offset: 1

Omar E. Pol, Apr 13 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A000040, A000079, A076274, A139286, A139288, A139289, A139290, A139291, A139292, A139293, A139294, A139306.

[2^(2*p-1)-1: p in PrimesUpTo(200)]; // Vincenzo Librandi, Dec 15 2010

Table[(2^(2 Prime[n] - 1) - 1), {n, 1, 20}] (* Vincenzo Librandi, May 24 2014 *)

a(9) corrected by Vincenzo Librandi, May 24 2014

A139290 2^(2p - 1)/4, where p is prime.

Original entry on oeis.org

2, 8, 128, 2048, 524288, 8388608, 2147483648, 34359738368, 8796093022208, 36028797018963968, 576460752303423488, 2361183241434822606848, 604462909807314587353088, 9671406556917033397649408

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Cf. A139286, A139287, A139288, A139289, A139290, A139292, A139293, A139294, A139306.

[2^(2*p-1)div 4: p in PrimesUpTo(200)]; // Vincenzo Librandi, Dec 15 2010

2^(2#-1)/4 & /@ Prime@ Range@ 15 (* Harvey P. Dale, Dec 16 2010 *)

a(n) = A139286(n)/4.

More terms from Jon E. Schoenfield, Jul 16 2010

A139288 2^(2p - 1)/2, where p is prime.

Original entry on oeis.org

4, 16, 256, 4096, 1048576, 16777216, 4294967296, 68719476736, 17592186044416, 72057594037927936, 1152921504606846976, 4722366482869645213696, 1208925819614629174706176, 19342813113834066795298816

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Cf. A139286, A139287, A139289, A139290, A139291, A139292, A139293, A139294, A139306.

Table[2^(2p-1)/2,{p,Prime[Range[20]]}] (* Harvey P. Dale, Jun 21 2021 *)

a(n)=A139286(n)/2.

More terms from Jon E. Schoenfield, Jul 16 2010

A139289 (2^(2p - 1)/2)-1, where p is prime.

Original entry on oeis.org

3, 15, 255, 4095, 1048575, 16777215, 4294967295, 68719476735, 17592186044415, 72057594037927935, 1152921504606846975, 4722366482869645213695, 1208925819614629174706175, 19342813113834066795298815, 4951760157141521099596496895, 20282409603651670423947251286015, 83076749736557242056487941267521535

Offset: 1

Omar E. Pol, Apr 13 2008

nonn

Floris P. van Doorn and Jasper Mulder, Table of n, a(n) for n=1..260.

Cf. A139286, A139287, A139288, A139290, A139291, A139292, A139293, A139294, A139306.

Table[(2^(2 Prime[p] - 1)/2) - 1, {p, 1, 20}] (* Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009 *)

a(n) = A139286(n)/2 - 1.

More terms from Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009

A139224 M(M-1)/2, where M is Mersenne prime A000668(n).

Original entry on oeis.org

3, 21, 465, 8001, 33542145, 8589737985, 137438167041, 2305843005992468481, 2658455991569831742348849606740148225, 191561942608236107294793377465333618488307184098607105

Offset: 1

Omar E. Pol, May 10 2008

nonn

Perfect number A000396(n) minus Mersenne prime A000668(n).

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000217, A000396, A000668, A036689, A139096, A139115, A139116, A139223, A139225, A139226, A139256, A139306.

a(n) = A000668(n)*(A000668(n)-1)/2.

a(n) = A000396(n)-A000668(n).

More terms from Max Alekseyev, Mar 09 2009

cp's OEIS Frontend

A139301 a(n) = (2^(2p - 1)/8)-1, where p is the n-th Mersenne prime A000668(n).

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A139302 a(n) = 2^(2p - 1)/16, where p is the n-th Mersenne prime A000668(n).

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A139303 a(n) = (2^(2p - 1)/16)-1, where p is the n-th Mersenne prime A000668(n).

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A139304 a(n) = 2^(2p - 1)/32, where p is the n-th Mersenne prime A000668(n).

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A139305 a(n) = (2^(2p - 1)/32)-1, where p is the n-th Mersenne prime A000668(n).

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A139287 2^(2p - 1) - 1, where p is prime.

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Magma

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A139290 2^(2p - 1)/4, where p is prime.

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Magma

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A139288 2^(2p - 1)/2, where p is prime.

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Mathematica

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A139289 (2^(2p - 1)/2)-1, where p is prime.

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