cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A138124 Initial digit of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 1, 6, 4, 6, 2, 1, 1, 3, 8, 8, 3, 2, 5, 7, 2, 1, 9, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 2, 3, 8, 6, 2, 4, 3, 6, 2, 4
Offset: 1

Views

Author

Omar E. Pol and Robert G. Wilson v, Apr 01 2008

Keywords

Comments

Also, initial digit of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Examples

			a(5)=4 because the 5th even superperfect number A061652(5) is 4096 and the initial digit of 4096 is 4.

Crossrefs

Cf. A000030, A077648, A019279, A061652, A135613, A135617, A138125.

Programs

  • Mathematica
    lst = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917}; f[n_] := Block[{pn = 2^(n - 1)}, Quotient[pn, 10^Floor[Log[10, pn]]]]; f@# & /@ (* Robert G. Wilson v, Apr 01 2008 *)

Extensions

a(13)-a(39) from Robert G. Wilson v, Apr 01 2008

A138867 First two digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 16, 64, 40, 65, 26, 10, 11, 30, 81, 85, 34, 26, 52, 73, 22, 12, 95, 14, 23, 17, 14, 21, 22, 20, 42, 26, 26, 25, 37, 87, 64, 20, 40, 31, 63, 21, 46, 62, 14, 61, 15, 62, 10, 84, 15
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, first two digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Crossrefs

Cf. A019279, A061652, A138862, A138868, A138869, A138873.

Extensions

a(12)-a(31) from R. J. Mathar, Feb 05 2010
a(32)-a(47) from Jinyuan Wang, Mar 14 2020

A138870 First 3 digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 16, 64, 409, 655, 262, 107, 115, 309, 811, 850, 343, 265, 520, 737, 223, 129, 953, 142, 239, 173, 140, 215, 224, 201, 427, 268, 260, 256, 373, 870, 647, 206, 407, 311, 637, 218, 462, 629, 149, 610, 157, 622, 101, 849, 158
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, first 3 digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Crossrefs

Cf. A019279, A061652, A138864, A138867, A138871, A138872, A138876.

Extensions

a(12)-a(31) from R. J. Mathar, Feb 05 2010
a(32)-a(41) from Max Alekseyev, Feb 11 2012
a(42)-a(47) from Jinyuan Wang, Mar 14 2020

A153475 Sum of the first n even superperfect numbers (A061652).

Original entry on oeis.org

2, 6, 22, 86, 4182, 69718, 331862, 1074073686, 1152921505680920662, 309485010974266574405701718, 81129947899617655962363410845782, 85070672860182515483499614221352898646
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008

Keywords

Comments

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

Crossrefs

Cf. A092336, A019279, A061652, A153474, A153476.

Formula

a(n) = A061652(1) + A061652(2) + ... + A061652(n). - Max Alekseyev, Jul 27 2009

Extensions

More terms from Max Alekseyev, Jul 27 2009

A138834 Bisection of even superperfect numbers A061652.

Original entry on oeis.org

2, 16, 4096, 262144, 1152921504606846976, 81129638414606681695789005144064
Offset: 1

Views

Author

Omar E. Pol, Apr 06 2008

Keywords

Comments

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

Links

Crossrefs

Cf. A019279, A061652, A099057, A099058, A134721, A134722.

Formula

a(n) = A061652(2*n-1). - Jinyuan Wang, Mar 14 2020

A138868 Last two digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 16, 64, 96, 36, 44, 24, 76, 56, 64, 64, 76, 64, 44, 4, 76, 36, 96, 4, 56, 76, 96, 36, 76, 56, 36, 4, 4, 56, 24, 44, 96, 64, 56, 76, 36, 96, 36, 24, 4, 24, 36, 36, 64, 76, 56
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, last two digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Crossrefs

Cf. A019279, A061652, A138867, A138869, A138870, A138874.

Extensions

More terms from Jinyuan Wang, Mar 14 2020

A138869 Concatenation of first two digits and last two digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

22, 44, 1616, 6464, 4096, 6536, 2644, 1024, 1176, 3056, 8164, 8564, 3476, 2664, 5244, 7304, 2276, 1236, 9596, 1404, 2356, 1776, 1496, 2136, 2276, 2056, 4236, 2604, 2604, 2556, 3724, 8744, 6496, 2064, 4056, 3176, 6336, 2196, 4636, 6224, 1404, 6124, 1536, 6236, 1064, 8476, 1556
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, concatenation of first two digits and last two digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Crossrefs

Cf. A019279, A061652, A138863, A138867, A138868, A138875.

Extensions

More terms from Jinyuan Wang, Mar 14 2020

A138871 Last 3 digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 16, 64, 96, 536, 144, 824, 976, 56, 64, 864, 576, 64, 544, 504, 176, 536, 496, 304, 56, 776, 96, 736, 376, 256, 336, 104, 504, 656, 224, 944, 296, 264, 856, 576, 136, 896, 536, 24, 704, 624, 936, 936, 464, 376, 256, 976
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, last 3 digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Crossrefs

Cf. A019279, A061652, A138865, A138867, A138870, A138872.

Formula

a(n) = 2^(A000043(n)-1) mod 1000. - Max Alekseyev, Feb 16 2024

Extensions

More terms from R. J. Mathar, Feb 05 2010
a(40)-a(41) from Max Alekseyev, Feb 11 2012
a(42)-a(47) from Jinyuan Wang, Mar 14 2020
a(48) from Max Alekseyev, Feb 16 2024

A138872 Concatenation of first 3 digits and last 3 digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

22, 44, 1616, 6464, 409096, 655536, 262144, 107824, 115976, 309056, 811064, 850864, 343576, 265064, 520544, 737504, 223176, 129536, 953496, 142304, 239056, 173776, 140096, 215736, 224376, 201256, 427336, 268104, 260504, 256656, 373224, 870944
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, concatenation of first 3 digits and last 3 digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Crossrefs

Cf. A019279, A061652, A138866, A138877, A138870, A138871.

Extensions

More terms from Max Alekseyev, Feb 11 2012

A138882 Triangle read by rows: row n lists divisors of n-th even superperfect number A061652(n).

Original entry on oeis.org

1, 2, 1, 2, 4, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 32, 64, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384
Offset: 1

Views

Author

Omar E. Pol, Apr 11 2008

Keywords

Comments

The number of divisors of n-th even superperfect number is equal to A000043(n), then row n has A000043(n) terms.
The sum of divisors of n-th even superperfect number is equal to n-th Mersenne prime A000668(n), then n-th row sum is equal to A000668(n).

Examples

			Triangle begins:
  1, 2
  1, 2, 4
  1, 2, 4, 8, 16
  1, 2, 4, 8, 16, 32, 64
  1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096
  ...
==============================================================
..... Mersenne ..............................................
....... prime ...............................................
n ... A000668(n) = Sum of divisors of A061652(n) .............
==============================================================
1 ........ 3 ... = 1+2
2 ........ 7 ... = 1+2+4
3 ....... 31 ... = 1+2+4+8+16
4 ...... 127 ... = 1+2+4+8+16+32+64
5 ..... 8191 ... = 1+2+4+8+16+32+64+128+256+512+1024+2048+4096

Links

Crossrefs

Cf. A000005, A000043, A000203, A000668, A019279, A061652, A133031.

Programs

  • Mathematica
    Flatten[Divisors[2^(MersennePrimeExponent[Range[7]]-1)]] (* Harvey P. Dale, Apr 28 2022 *)
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