A240092 Sequence of numbers starting at 1 and giving a new maximum record for sigma(n) modulo n (A054024), where sigma(n) is the sum of divisors of n (A000203).

1, 2, 4, 8, 10, 14, 16, 26, 32, 44, 50, 52, 60, 64, 76, 92, 105, 110, 128, 136, 152, 170, 184, 225, 230, 232, 248, 256, 296, 315, 336, 376, 410, 424, 470, 472, 484, 512, 568, 584, 592, 630, 656, 688, 752, 792, 848, 884, 944, 976, 988, 1012, 1024, 1072, 1136

Offset

1,2

Comments

If m is a power of 2, then sigma(m) = 2*m - 1 = m - 1, so sigma(m) == m-1 modulo m, thus giving a new record for A054024, hence A000079 is a subsequence.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

From the first terms of A054024 : 0, 1, 1, 3, 1, 0, 1, 7, 4, 8, 1, 4, 1, 10, ... we can see the records 0, 1, 3, 7, 8, 10, ... obtained for 1, 2, 4, 8, 10, ....

Mathematica

DeleteDuplicates[Table[{n, Mod[DivisorSigma[1, n], n]}, {n, 1200}], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Jun 09 2024 *)

Prog

(PARI) lista(nn) = {rec = -1; for (n=1, nn, sm = sigma(n) % n; if (sm > rec, rec = sm; print1(n, ", "); ); ); }

Crossrefs

Cf. A000079, A000203, A054024.

Sequence in context: A226872 A132895 A125499 * A153974 A290476 A189670

Adjacent sequences: A240089 A240090 A240091 * A240093 A240094 A240095

Keyword

nonn

Author

Michel Marcus, Apr 01 2014

Status

approved