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 A327635 Numbers k such that both k and k+1 are infinitary abundant numbers (A129656). 9
 21735, 21944, 43064, 58695, 188055, 262184, 414855, 520695, 567944, 611415, 687015, 764504, 792855, 809864, 812889, 833624, 874664, 911624, 945944, 976184, 991304, 1019655, 1026375, 1065015, 1073709, 1157624, 1201095, 1218944, 1248344, 1254015, 1272375, 1272704 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The least k such that k, k+1 and k+2 are all infinitary abundant numbers is a(75976) = 2666847104. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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). MATHEMATICA f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); isigma = 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 CROSSREFS Cf. A049417, A127666, A129656. Cf. A096399, A292704, A318167. Sequence in context: A232419 A251033 A318167 * A274807 A348606 A185863 Adjacent sequences: A327632 A327633 A327634 * A327636 A327637 A327638 KEYWORD nonn AUTHOR Amiram Eldar, Sep 20 2019 STATUS approved

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Last modified October 2 11:50 EDT 2023. Contains 365833 sequences. (Running on oeis4.)