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%I #14 Sep 21 2019 02:49:30
%S 21735,21944,43064,58695,188055,262184,414855,520695,567944,611415,
%T 687015,764504,792855,809864,812889,833624,874664,911624,945944,
%U 976184,991304,1019655,1026375,1065015,1073709,1157624,1201095,1218944,1248344,1254015,1272375,1272704
%N Numbers k such that both k and k+1 are infinitary abundant numbers (A129656).
%C The least k such that k, k+1 and k+2 are all infinitary abundant numbers is a(75976) = 2666847104.
%H Amiram Eldar, <a href="/A327635/b327635.txt">Table of n, a(n) for n = 1..10000</a>
%e 21735 is in the sequence since both 21735 and 21736 are infinitary abundant: isigma(21735) = 46080 > 2 * 21735, and isigma(21736) = 50400 > 2 * 21736 (isigma is the sum of infinitary divisors, A049417).
%t 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] > 2n; s={}; ab1 = 0; Do[ab2 = abQ[n]; If[ab1 && ab2, AppendTo[s, n-1]]; ab1 = ab2, {n, 2, 10^5}]; s
%Y Cf. A049417, A127666, A129656.
%Y Cf. A096399, A292704, A318167.
%K nonn
%O 1,1
%A _Amiram Eldar_, Sep 20 2019
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