A139228 -id:A139228 - cp's OEIS frontend

A139237 Second differences of even superperfect numbers A061652, divided by 2.

5, 18, 1992, 28704, 67584, 536641536, 576460751229812736, 154742503757751030292414464, 40564509722294095963578081214464, 42535214735633635831150802674328272896

Offset: 1

Omar E. Pol, Apr 18 2008

nonn

Second differences of Mersenne primes A000668, divided by 4 (see A139232).

Also, second differences of superperfect numbers A019279, divided by 2, if there are no odd superperfect numbers.

Paolo Xausa, Table of n, a(n) for n = 1..16

Cf. A000668, A019279, A061652, A139228, A139229, A139230, A139231, A139232, A139233, A139234, A139235, A139236.

Differences[2^MersennePrimeExponent[Range[14]]-1,2]/4 (* Paolo Xausa, Oct 20 2023 *)

a(n) = A139236(n)/2.

More terms from Michel Marcus, Jul 09 2017

A139229 First differences of perfect numbers A000396, divided by 2.

Original entry on oeis.org

11, 234, 3816, 16771104, 4278159360, 64424411136, 1152921435350630400, 1329227995784915871174424803906945024, 95780971304118052318168693257235946738152352797163520

Offset: 1

Omar E. Pol, Apr 19 2008

nonn

Paolo Xausa, Table of n, a(n) for n = 1..14

Cf. A000396, A139228, A139230, A139231, A139232, A139233, A139234, A139235, A139236, A139237.

Differences[Select[Range[10000], DivisorSigma[1, #] == 2# &]]/2 (* Alonso del Arte, Mar 05 2020 *)
Differences[PerfectNumber[Range[12]]]/2 (* Paolo Xausa, Oct 20 2023 *)

a(n) = A139228(n)/2.

a(6)-a(9) from A139228(n)/2 by Jinyuan Wang, Mar 04 2020

A139230 Second differences of perfect numbers A000396.

Original entry on oeis.org

446, 7164, 33534576, 8522776512, 120292503552, 2305842741852438528, 2658455991569831740043006737112629248, 191561942608236101977881394944640151127455097780436992

Offset: 1

Omar E. Pol, Apr 19 2008

nonn

Paolo Xausa, Table of n, a(n) for n = 1..13

Cf. A000396, A139228, A139229, A139231, A139232, A139233, A139234, A139235, A139236, A139237.

Differences[PerfectNumber[Range[12]],2] (* Paolo Xausa, Oct 20 2023 *)

a(n) = A139228(n+1) - A139228(n). - Jinyuan Wang, Mar 04 2020

a(5)-a(8) from Jinyuan Wang, Mar 04 2020

A139231 First differences of Mersenne primes A000668.

Original entry on oeis.org

4, 24, 96, 8064, 122880, 393216, 2146959360, 2305843007066210304, 618970017336847128235868160, 162258657859193720701440560726016, 170141021201192402518323912137873817600

Offset: 1

Omar E. Pol, Apr 18 2008

nonn

			a(1)=4 because A000668(1)=3 and A000668(2)=7 then 7-3 = 4.

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

Cf. A000668, A139228, A139229, A139230, A139232, A139233, A139234, A139235, A139236, A139237.

A000668 := Select[2^Range[1000] - 1, PrimeQ]; Table[A000668[[n + 1]] - A000668[[n]], {n, 1, 10}] (* G. C. Greubel, Oct 03 2017 *)
Differences[2^MersennePrimeExponent[Range[20]]-1] (* Harvey P. Dale, Mar 31 2022 *)

a=0; b=0; forprime(p=1, 1e2, if(ispseudoprime(2^p-1) && a==0, a=2^p-1); if(ispseudoprime(2^p-1) && a!=0, b=2^p-1; if(a!=b, print1(b-a, ", ")); a=b)) \\ Felix Fröhlich, Aug 12 2014

a(n) = A000668(n+1) - A000668(n).

a(8)-a(11) from Felix Fröhlich, Aug 12 2014

A139232 Second differences of Mersenne primes A000668.

Original entry on oeis.org

20, 72, 7968, 114816, 270336, 2146566144, 2305843004919250944, 618970015031004121169657856, 162258038889176383854312324857856, 170140858942534543324603210697313091584

Offset: 1

Omar E. Pol, Apr 19 2008

nonn

Second differences of even superperfect numbers, multiplied by 2 (see A139236).

G. C. Greubel, Table of n, a(n) for n = 1..16

Cf. A000668, A019279, A061652, A139228, A139229, A139230, A139231, A139233, A139234, A139235, A139236, A139237.

A000668 := Select[2^Range[1000] - 1, PrimeQ]; Table[A000668[[n + 2]] - 2*A000668[[n + 1]] + A000668[[n]], {n, 1, 6}] (* G. C. Greubel, Oct 03 2017 *)
Differences[2^MersennePrimeExponent[Range[14]]-1,2] (* Paolo Xausa, Oct 20 2023 *)

a(n) = A139236(n)*2.

Terms a(7) - a(10) added by G. C. Greubel, Oct 03 2017

A139233 Second differences of perfect numbers A000396, divided by 2.

Original entry on oeis.org

223, 3582, 16767288, 4261388256, 60146251776, 1152921370926219264, 1329227995784915870021503368556314624, 95780971304118050988940697472320075563727548890218496

Offset: 1

Omar E. Pol, Apr 19 2008

nonn

Paolo Xausa, Table of n, a(n) for n = 1..13

Cf. A000396, A139228, A139229, A139230, A139231, A139232, A139234, A139235, A139236, A139237.

Differences[PerfectNumber[Range[12]],2]/2 (* Paolo Xausa, Oct 20 2023 *)

a(n) = A139230(n)/2.

a(5)-a(8) from Jinyuan Wang, Mar 04 2020

A139235 First differences of even superperfect numbers A061652, divided by 2.

Original entry on oeis.org

1, 6, 24, 2016, 30720, 98304, 536739840, 576460751766552576, 154742504334211782058967040, 40564664464798430175360140181504, 42535255300298100629580978034468454400

Offset: 1

Omar E. Pol, Apr 18 2008

nonn

First differences of Mersenne primes A000668, divided by 4 (see A139231).

Also, first differences of superperfect numbers A019279, divided by 2, if there are no odd superperfect numbers.

Paolo Xausa, Table of n, a(n) for n = 1..17

Cf. A000668, A019279, A061652, A139228, A139229, A139230, A139231, A139232, A139233, A139234, A139236, A139237.

Differences[2^MersennePrimeExponent[Range[14]]-1]/4 (* Paolo Xausa, Oct 20 2023 *)

a(n) = A139234(n)/2.

a(8)-a(11) from Jinyuan Wang, Mar 04 2020

A139236 Second differences of even superperfect numbers A061652.

Original entry on oeis.org

10, 36, 3984, 57408, 135168, 1073283072, 1152921502459625472, 309485007515502060584828928, 81129019444588191927156162428928, 85070429471267271662301605348656545792

Offset: 1

Omar E. Pol, Apr 18 2008

nonn

Second differences of Mersenne primes A000668, divided by 2 (see A139232).

Also, second differences of superperfect numbers A019279, if there are no odd superperfect numbers.

Jinyuan Wang, Table of n, a(n) for n = 1..16

Cf. A000668, A019279, A061652, A139228, A139229, A139230, A139231, A139232, A139233, A139234, A139235, A139237.

Differences[2^(Select[Range[512],PrimeQ[2^#-1]&]-1),2] (* Harvey P. Dale, Oct 15 2017 *)

a(n) = A139234(n+1) - A139234(n).

a(6) corrected and more terms from Joerg Arndt, Jul 09 2017

A139234 First differences of even superperfect numbers A061652.

Original entry on oeis.org

2, 12, 48, 4032, 61440, 196608, 1073479680, 1152921503533105152, 309485008668423564117934080, 81129328929596860350720280363008, 85070510600596201259161956068936908800

Offset: 1

Omar E. Pol, Apr 18 2008

nonn

First differences of Mersenne primes A000668, divided by 2 (see A139231).

Also, first differences of superperfect numbers A019279, if there are no odd superperfect numbers.

			a(2) = 12 because A061652(2) = 4 and A061652(3) = 16 then 16 - 4 = 12.

Cf. A000668, A019279, A061652, A139228, A139229, A139230, A139231, A139232, A139233, A139235, A139236, A139237.

Differences[Table[2^(MersennePrimeExponent[n]-1),{n,12}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 18 2020 *)

a(n) = A061652(n+1) - A061652(n) = A139231(n)/2. Also, a(n) = A019279(n+1) - A019279(n), if there are no odd superperfect numbers.

a(8)-a(11) from A139231(n)/2 by Jinyuan Wang, Mar 04 2020

A139238 First differences of Mersenne numbers A001348.

Original entry on oeis.org

4, 24, 96, 1920, 6144, 122880, 393216, 7864320, 528482304, 1610612736, 135291469824, 2061584302080, 6597069766656, 131941395333120, 8866461766385664, 567453553048682496, 1729382256910270464, 145268109580462718976, 2213609288845146193920

Offset: 1

Omar E. Pol, Apr 19 2008

Also, first differences of 2^prime(n) = A034785(n). - Wesley Ivan Hurt, Jul 02 2014

			a(2)=24 because A001348(2)=7 and A001348(2+1)=31 then 31-7 = 24.

Felix Fröhlich, Table of n, a(n) for n = 1..59

Cf. A001348, A139228, A139231, A139234, A139239, A139240, A139241, A139242, A139243.

Cf. A034785.

A139238:=n->2^ithprime(n+1)-2^ithprime(n): seq(A139238(n), n=1..20); # Wesley Ivan Hurt, Jul 02 2014

Table[2^Prime[n + 1] - 2^Prime[n], {n, 20}] (* Wesley Ivan Hurt, Jul 02 2014 *)

for(n=1, 20, d=2^prime(n+1)-2^prime(n); print1(d, ", ")) \\ Felix Fröhlich, Jun 30 2014

a(n) = A001348(n+1) - A001348(n).

a(n) = A034785(n+1) - A034785(n). - Wesley Ivan Hurt, Jul 02 2014

a(10)-a(19) from Felix Fröhlich, Jun 30 2014

cp's OEIS Frontend

A139237 Second differences of even superperfect numbers A061652, divided by 2.

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A139229 First differences of perfect numbers A000396, divided by 2.

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A139230 Second differences of perfect numbers A000396.

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A139231 First differences of Mersenne primes A000668.

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A139232 Second differences of Mersenne primes A000668.

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A139233 Second differences of perfect numbers A000396, divided by 2.

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A139235 First differences of even superperfect numbers A061652, divided by 2.

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A139236 Second differences of even superperfect numbers A061652.

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