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 A318167 Numbers k such that both k and k+1 are bi-unitary abundant numbers. 10
 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 July 12 19:36 EDT 2024. Contains 374252 sequences. (Running on oeis4.)