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A318167 Numbers k such that both k and k+1 are bi-unitary abundant numbers. 8
21735, 21944, 43064, 49664, 58695, 76544, 106784, 135135, 144584, 160544, 188055, 209055, 227744, 256095, 262184, 300104, 345344, 348704, 382304, 387584, 407295, 409184, 414855, 437535, 498015, 520695, 560384, 567944, 611415, 679455, 687015, 705375, 709695 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The bi-unitary version of A096399.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

21735 is in the sequence since both 21735 and 21736 are bi-unitary abundant numbers.

MATHEMATICA

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] := DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bAbundantQ[n_] := bsigma[n] > 2 n; seq={}; n=1; While[Length[seq]<32, If[bAbundantQ[n] && bAbundantQ [n+1], AppendTo[seq, n]]; n++]; seq

PROG

(PARI) a188999(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; e = f[i, 2]; f[i, 1] = if (e % 2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)); f[i, 2] = 1; ); factorback(f); }

isok(n) = (a188999(n) > 2*n) && (a188999(n+1) > 2*(n+1)); \\ Michel Marcus, Aug 21 2018

CROSSREFS

Cf. A096399 (analog for sigma), A188999 (bi-unitary sigma).

Cf. A292982 (bi-unitary abundant), A293186 (odd bi-unitary abundant).

Sequence in context: A232121 A232419 A251033 * A327635 A274807 A348606

Adjacent sequences:  A318164 A318165 A318166 * A318168 A318169 A318170

KEYWORD

nonn

AUTHOR

Amiram Eldar, Aug 20 2018

STATUS

approved

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Last modified September 27 03:24 EDT 2022. Contains 357051 sequences. (Running on oeis4.)