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A327635 Numbers k such that both k and k+1 are infinitary abundant numbers (A129656). 5
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] = 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 A185863 A265614

Adjacent sequences:  A327632 A327633 A327634 * A327636 A327637 A327638

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 20 2019

STATUS

approved

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Last modified May 9 10:52 EDT 2021. Contains 343732 sequences. (Running on oeis4.)