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

Author

Amiram Eldar, Aug 11 2023

Keywords

• nonn

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.

Crossrefs

Subsequence of A181487.

Cf. A096399, A096536, A118372.

Programs

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]

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<M. F. Hasler at A181487