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

Author

Amiram Eldar, Aug 20 2018

Keywords

• nonn

Comments

The bi-unitary version of A096399.

Examples

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

Links

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

Crossrefs

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

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

Programs

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

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