cp's OEIS Frontend

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

%I A318167 #11 Jan 18 2020 03:13:21
%S A318167 21735,21944,43064,49664,58695,76544,106784,135135,144584,160544,
%T A318167 188055,209055,227744,256095,262184,300104,345344,348704,382304,
%U A318167 387584,407295,409184,414855,437535,498015,520695,560384,567944,611415,679455,687015,705375,709695
%N A318167 Numbers k such that both k and k+1 are bi-unitary abundant numbers.
%C A318167 The bi-unitary version of A096399.
%H A318167 Amiram Eldar, <a href="/A318167/b318167.txt">Table of n, a(n) for n = 1..10000</a>
%e A318167 21735 is in the sequence since both 21735 and 21736 are bi-unitary abundant numbers.
%t A318167 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
%o A318167 (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); }
%o A318167 isok(n) = (a188999(n) > 2*n) && (a188999(n+1) > 2*(n+1)); \\ _Michel Marcus_, Aug 21 2018
%Y A318167 Cf. A096399 (analog for sigma), A188999 (bi-unitary sigma).
%Y A318167 Cf. A292982 (bi-unitary abundant), A293186 (odd bi-unitary abundant).
%K A318167 nonn
%O A318167 1,1
%A A318167 _Amiram Eldar_, Aug 20 2018