A364975 Admirable numbers (A111592) with a record gap to the next admirable number.

12, 30, 42, 88, 120, 140, 186, 534, 678, 6774, 7962, 77118, 94108, 152826, 478194, 662154, 935564, 1128174, 2028198, 6934398, 7750146, 8330924, 9984738, 10030804, 22956114, 62062566, 151040622, 284791602, 732988732, 804394974, 1151476732, 9040886574, 31302713634

Offset

1,1

Comments

The corresponding record gaps are 8, 10, 12, 14, 18, 34, 36, 48, 84, 132, 204, 216, 254, 312, 348, 360, 392, 468, 516, 528, 552, 598, 624, 638, 828, 852, 936, 1056, 1082, 1128, 1454, 1692, 1752, ... .

Links

Table of n, a(n) for n=1..33.

Example

The first 5 admirable numbers are 12, 20, 24, 30 and 40. The differences between these terms are 8, 4, 6 and 10. The record gaps, 8 and 10, occur after the terms 12 and 30, which are the first two terms of this sequence.

Mathematica

admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];
seq[kmax_] := Module[{s = {}, m = 12, dm = 0}, Do[If[admQ[k], d = k - m; If[d > dm, dm = d; AppendTo[s, m]]; m = k], {k, m + 1, kmax}]; s]; seq[10^6]

Prog

(PARI) isadm(n) = {my(ab=sigma(n)-2*n); ab>0 && ab%2 == 0 && ab/2 < n && n%(ab/2) == 0; }
lista(kmax) = {my(m = 12, dm = 0); for(k = m+1, kmax, if(isadm(k), d = k - m; if(d > dm, dm = d; print1(m, ", ")); m = k)); }

Crossrefs

Cf. A111592, A364727.

Similar sequences: A306953, A330870, A334418, A334419, A334883, A363296.

Sequence in context: A333840 A145470 A108278 * A298077 A135502 A256620

Adjacent sequences: A364972 A364973 A364974 * A364976 A364977 A364978

Keyword

nonn

Author

Amiram Eldar, Aug 15 2023

Status

approved