A139237
Second differences of even superperfect numbers A061652, divided by 2.
Original entry on oeis.org
5, 18, 1992, 28704, 67584, 536641536, 576460751229812736, 154742503757751030292414464, 40564509722294095963578081214464, 42535214735633635831150802674328272896
Offset: 1
Cf.
A000668,
A019279,
A061652,
A139228,
A139229,
A139230,
A139231,
A139232,
A139233,
A139234,
A139235,
A139236.
A139228
First differences of perfect numbers A000396.
Original entry on oeis.org
22, 468, 7632, 33542208, 8556318720, 128848822272, 2305842870701260800, 2658455991569831742348849607813890048, 191561942608236104636337386514471893476304705594327040
Offset: 1
a(1) = 22 because 6 and 28 are the first two perfect numbers, and their difference is 28 - 6 = 22.
- Paolo Xausa, Table of n, a(n) for n = 1..14
- Philippe Ellia, On the distance between perfect numbers, arXiv:1210.0450 [math.NT], 2012.
- Florian Luca, Problem 10711, Amer. Math. Monthly, Vo. 106, No. 2 (1999) p. 166; Can Two Consecutive Numbers Both Be Perfect?, solution by Francis B. Coghlan, ibid., Vol. 108, No. 1 (2001), pp. 80-81.
- Florian Luca and Carl Pomerance, On the radical of a perfect number, New York Journal of Math., Vol. 16 (2010), pp. 23-30; alternative link.
- Florian Luca and Herman te Riele, phi and sigma: from Euler to Erdős, Nieuw Archief voor Wiskunde, Vol. 12, No. 5 (2011), pp. 31-36.
-
Differences[Select[Range[10000], DivisorSigma[1, #] == 2# &]] (* Alonso del Arte, Mar 05 2020 *)
Differences[PerfectNumber[Range[12]]] (* Paolo Xausa, Oct 20 2023 *)
A139230
Second differences of perfect numbers A000396.
Original entry on oeis.org
446, 7164, 33534576, 8522776512, 120292503552, 2305842741852438528, 2658455991569831740043006737112629248, 191561942608236101977881394944640151127455097780436992
Offset: 1
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
a(1)=4 because A000668(1)=3 and A000668(2)=7 then 7-3 = 4.
-
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
A139232
Second differences of Mersenne primes A000668.
Original entry on oeis.org
20, 72, 7968, 114816, 270336, 2146566144, 2305843004919250944, 618970015031004121169657856, 162258038889176383854312324857856, 170140858942534543324603210697313091584
Offset: 1
Cf.
A000668,
A019279,
A061652,
A139228,
A139229,
A139230,
A139231,
A139233,
A139234,
A139235,
A139236,
A139237.
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
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
Cf.
A000668,
A019279,
A061652,
A139228,
A139229,
A139230,
A139231,
A139232,
A139233,
A139234,
A139236,
A139237.
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
Cf.
A000668,
A019279,
A061652,
A139228,
A139229,
A139230,
A139231,
A139232,
A139233,
A139234,
A139235,
A139237.
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
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 *)
A139239
First differences of Mersenne numbers A001348, divided by 2.
Original entry on oeis.org
2, 12, 48, 960, 3072, 61440, 196608, 3932160, 264241152, 805306368, 67645734912, 1030792151040, 3298534883328, 65970697666560, 4433230883192832, 283726776524341248, 864691128455135232, 72634054790231359488, 1106804644422573096960, 3541774862152233910272, 297509088420787648462848
Offset: 1
Showing 1-10 of 10 results.
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