A318167 Numbers k such that both k and k+1 are bi-unitary abundant numbers.

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

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