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A358483 Numbers k such that k, k+1 and k+2 are all infinitary abundant numbers (A129656). 1
2666847104, 2695309694, 8207456894, 8967010688, 12147283070, 12491149670, 13911605630, 14126720894, 17238119624, 17238704768, 18420223094, 20922243110, 21786026624, 25118874494, 26079705728, 26979164288, 27257009624, 30000503168, 30478990904, 30832299134, 32892108248 (list; graph; refs; listen; history; text; internal format)
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 18 2022
STATUS
approved

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Last modified July 13 11:10 EDT 2024. Contains 374282 sequences. (Running on oeis4.)