A327635 Numbers k such that both k and k+1 are infinitary abundant numbers (A129656).

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

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 A348606 A185863

Adjacent sequences: A327632 A327633 A327634 * A327636 A327637 A327638

Keyword

nonn

Author

Amiram Eldar, Sep 20 2019

Status

approved