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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
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
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.)