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

Author

Amiram Eldar, Oct 22 2017

Keywords

• nonn
• fini
• more

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.

Examples

			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, ...
		

Crossrefs

Cf. A293186, A294025.

Programs

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

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

Extensions

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

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