A364861 Numbers k such that k and k+1 are both S-abundant numbers (A181487).

5984, 7424, 21944, 39375, 56924, 77175, 82004, 84524, 89775, 109395, 116655, 158235, 174824, 180495, 185535, 188055, 193544, 200024, 209055, 235935, 238095, 240344, 245024, 250964, 256095, 261260, 262184, 263024, 266475, 279279, 282975, 283815, 294975, 297296

Offset

1,1

Comments

De Koninck and Ivić found that the least number k such that k, k+1, and k+2 are 3 consecutive integers that are S-abundant numbers is 171078830 (which is also the first term of A096536).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Jean-Marie De Koninck and Aleksandar Ivić, On a sum of divisors problem, Publications de l'Institut Mathématique (Beograd), New Series, Vol. 64 (78) (1998), pp. 9-20.

Wikipedia, Granville number.

Mathematica

seq[kmax_] := Module[{s = {1}, a = {}, sum, q1 = False, q2}, Do[sum = Total[Select[Divisors[k], MemberQ[s, #] &]]; q2 = sum > k; If[!q2, AppendTo[s, k]]; If[q1 && q2, AppendTo[a, k-1]]; q1 = q2, {k, 2, kmax}]; a]; seq[40000]

Prog

(PARI) lista(nmax) = {my(c = 0, s, q1 = 0, q2); for(n=2, nmax, if(sumdiv(n, d, !bittest(c, d)*d) > 2*n, c+=1<<n; q2 = 1, q2 = 0); if(q1 && q2, print1(n-1, ", ")); q1 = q2) } \\ after M. F. Hasler at A181487

Crossrefs

Subsequence of A181487.

Cf. A096399, A096536, A118372.

Sequence in context: A176374 A282191 A328327 * A237011 A274362 A233871

Adjacent sequences: A364858 A364859 A364860 * A364862 A364863 A364864

Keyword

nonn

Author

Amiram Eldar, Aug 11 2023

Status

approved