A358483 Numbers k such that k, k+1 and k+2 are all infinitary abundant numbers (A129656).

2666847104, 2695309694, 8207456894, 8967010688, 12147283070, 12491149670, 13911605630, 14126720894, 17238119624, 17238704768, 18420223094, 20922243110, 21786026624, 25118874494, 26079705728, 26979164288, 27257009624, 30000503168, 30478990904, 30832299134, 32892108248

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..456 (terms below 10^12)

Example

2666847104 is in the sequence since 2666847104, 2666847105 and 2666847106 are all infinitary abundant numbers (A129656): isigma(2666847104) = 5401952640 > 2 * 2666847104, isigma(2666847105) = 5374656000 > 2 * 2666847105, and isigma(2666847106) = 5419376640 > 2 * 2666847106 (isigma is the sum of infinitary divisors, A049417).

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); isigma[1] = 1; isigma[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) + 1); abQ[n_] := isigma[n] > 2*n; v = Cases[Import["https://oeis.org/A096536/b096536.txt", "Table"], {_, _}][[;; , 2]]; Select[v, And @@ abQ /@ (# + {0, 1, 2}) &]

Crossrefs

Subsequence of A096536, A129656 and A327635.

Cf. A049417.

Sequence in context: A028521 A064163 A022230 * A034648 A274816 A216902

Adjacent sequences: A358480 A358481 A358482 * A358484 A358485 A358486

Keyword

nonn

Author

Amiram Eldar, Nov 18 2022

Status

approved