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.

Showing 1-4 of 4 results.

A275996 Numbers n whose abundance is 64: sigma(n) - 2n = 64.

Original entry on oeis.org

108, 220, 6808, 8968, 14008, 24448, 66928, 552568, 786208, 1020568, 5303488, 8229568, 10001848, 133685248, 499722448, 2608895488, 4733164768, 7163795488, 13707973408, 14468025568, 16122444736, 27339731968, 34351218688, 34672397728, 35371084288, 69657461248
Offset: 1

Views

Author

Timothy L. Tiffin, Aug 16 2016

Keywords

Comments

Any term x = a(m) of this sequence can be used with any term y of A275997 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable.
The smallest amicable pair is (220, 284) = (a(2), A275997(2)) = (A063990(1), A063990(2)), where 284 - 220 = 64 is the abundance of 220 and the deficiency of 284.
The amicable pair (66928, 66992) = (a(7), A275997(11)) = (A063990(18), A063990(19)), and 66992 - 66928 = 64 is the abundance of 66928 and the deficiency of 66992.

Examples

			a(1) = 108, since sigma(108) - 2*108 = 280 - 216 = 64.

Links

Crossrefs

Subsequence of A005101.
Cf. A002025, A063990, A275997, A088831, A088832, A088833, A141547, A175989, A275701, A066539, A259180.

Programs

  • PARI
    isok(n) = sigma(n) - 2*n == 64; \\ Michel Marcus, Dec 30 2016

Extensions

a(14)-a(15) from Michel Marcus, Dec 30 2016
a(16)-a(21) from Lars Blomberg, Jan 12 2017
Terms a(22) onward from Max Alekseyev, Aug 27 2025

A292626 Numbers k whose abundance is 128: sigma(k) - 2*k = 128.

Original entry on oeis.org

860, 5336, 6536, 9656, 16256, 55796, 70864, 98048, 361556, 776096, 2227616, 4145216, 4498136, 4632896, 8124416, 13086016, 34869056, 38546576, 150094976, 172960856, 196066256, 962085536, 1080008576, 1733780336, 1844788112, 2143256576, 2531343872, 2986104064, 9677743616, 11276687456, 17104503968, 20680182272, 21568135616
Offset: 1

Views

Author

Fabian Schneider, Sep 20 2017

Keywords

Links

Crossrefs

Subsequence of A259174.
Deficiency k: A191363 (k=2), A125246 (k=4), A141548 (k=6), A125247 (k=8), A101223 (k=10), A141549 (k=12), A141550 (k=14), A125248 (k=16), A223608 (k=18), A223607 (k=20), A223606 (k=22), A385255(k=24), A275702 (k=26), A387352 (k=32), A275997 (k=64).
Abundance k: A088831 (k=2), A088832 (k=4), A087167 (k=6), A088833 (k=8), A223609 (k=10), A141545 (k=12), A141546 (k=14), A141547 (k=16), A223610 (k=18), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64).

Programs

  • Mathematica
    fQ[n_] := DivisorSigma[1, n] == 2 n + 128; Select[ Range@ 10^8, fQ] (* Robert G. Wilson v, Nov 19 2017 *)
  • PARI
    isok(n) = sigma(n) - 2*n == 128; \\ Michel Marcus, Sep 20 2017

Extensions

a(9)-a(18) from Michel Marcus, Sep 20 2017
a(19)-a(24), a(26), a(29)-a(30), a(33) from Robert G. Wilson v, Nov 20 2017
Missing terms a(25), a(27)-a(28), a(31)-a(32) inserted and terms a(34) onward added by Max Alekseyev, Aug 30 2025

A387352 Numbers m with deficiency 32: sigma(m) - 2*m = -32.

Original entry on oeis.org

250, 376, 1276, 12616, 20536, 396916, 801376, 1297312, 8452096, 33721216, 40575616, 59376256, 89397016, 99523456, 101556016, 150441856, 173706136, 269096704, 283417216, 500101936, 1082640256, 1846506832, 15531546112, 34675557856, 136310177392, 136783784608
Offset: 1

Views

Author

Max Alekseyev, Aug 27 2025

Keywords

Comments

Contains numbers 2^(k-1)*(2^k + 31) for k in A247952.

Links

Crossrefs

Deficiency k: A191363 (k=2), A125246 (k=4), A141548 (k=6), A125247 (k=8), A101223 (k=10), A141549 (k=12), A141550 (k=14), A125248 (k=16), A223608 (k=18), A223607 (k=20), A223606 (k=22), A385255(k=24), A275702 (k=26), A275997 (k=64).
Abundance k: A088831 (k=2), A088832 (k=4), A087167 (k=6), A088833 (k=8), A223609 (k=10), A141545 (k=12), A141546 (k=14), A141547 (k=16), A223610 (k=18), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64), A292626 (k=128).
Cf. A247952.

A292557 a(n) is the smallest number k such that 2k - sigma(k) = 2^n.

Original entry on oeis.org

3, 5, 22, 17, 250, 134, 262, 257, 6556, 4124, 10330, 8198, 91036, 19649, 65542, 65537, 1442716, 524294, 1363258, 4194332, 4411642, 16442342, 16866106, 22075325, 156791188, 536871032, 2160104368, 536870918, 1074187546, 2147483654, 4295862586, 19492545788
Offset: 1

Views

Author

XU Pingya, Sep 19 2017

Keywords

Comments

Primes of the form 2^n+1, i.e., Fermat primes (A019434) are terms of this sequence.
For n > 32, a(n) > 2 * 10^10.

Examples

			sigma(20) - 2*20 = 2^1, a(1) = 20.
sigma(108) - 2*108 = 64 = 2^6, a(6) = 108.

Crossrefs

Cf. A019434, A033879, A125246, A125247, A125248, A191363, A275997.

Programs

  • Mathematica
    Table[k = 1; While[Log[2, 2k - DivisorSigma[1, k]] != n, k++]; k, {n, 31}]
  • PARI
    a(n) = my(k=1); while(2*k - sigma(k) != 2^n, k++); k; \\ Michel Marcus, Sep 19 2017
Showing 1-4 of 4 results.

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