A294027 Odd bi-unitary abundant numbers with a record small gap to the next term odd bi-unitary abundant number.

945, 8505, 15015, 19305, 21735, 33345, 34125, 21961263753, 39891817245

Offset

1,1

Comments

The corresponding gaps are 7560, 1890, 1050, 330, 210, 150, 30, 12, 6.

The upper ends are 8505, 10395, 16065, 19635, 21945, 33495, 34155, 21961263765, 39891817251.

The bi-unitary version of A294025.

Links

Table of n, a(n) for n=1..9.

Example

Odd bi-unitary abundant numbers are 945, 8505, 10395, 12285, 15015, 16065, 17955, 19305, 19635, 21735, 21945, ...
Their differences are 7560, 1890, 1890, 2730, 1050, 1890, 1350, 330, 2100, 210, ...
The records of small differences are 7560, 1890, 1050, 330, 210, ...
And the corresponding terms are 945, 8505, 15015, 19305, 21735, ...

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] := DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bOddAbundantQ[n_] := OddQ[n] && bsigma[n] > 2 n; s = Select[Range[1000000], bOddAbundantQ]; a = {}; dmin = 50000; Do[d = s[[j + 1]] - s[[j]]; If[d < dmin, AppendTo[a, s[[j]]]; dmin = d], {j, 1, Length[s] - 1}]; a

Prog

(PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
biudivs(n) = select(x->(gcud(x, n/x)==1), divisors(n));
biusig(n) = vecsum(biudivs(n));
isok(n) = (n % 2) && (biusig(n) > 2*n);
lista(nn) = {last = 0; gap = oo; forstep(n=1, nn, 2, if (isok(n), if (last, if (n - last < gap, print1(last, ", "); gap = n - last)); last = n; ); ); } \\ Michel Marcus, Dec 15 2017

Crossrefs

Cf. A293186, A294025.

Sequence in context: A294025 A275449 A293186 * A127666 A274756 A335053

Adjacent sequences: A294024 A294025 A294026 * A294028 A294029 A294030

Keyword

nonn,fini,more

Author

Amiram Eldar, Oct 22 2017

Extensions

a(1) added by Amiram Eldar, Aug 22 2018.

a(8)-a(9) from Giovanni Resta, Aug 22 2018

Status

approved