A294026 Odd unitary abundant numbers with a record small gap to the next odd unitary abundant number.

15015, 19635, 21945, 25935, 33495, 1752135, 1915095, 1915305, 119104635, 134877405

Offset: 1

Author

Amiram Eldar, Oct 22 2017

Keywords

• nonn
• fini
• more

Comments

The corresponding gaps are 4620, 2310, 1260, 630, 420, 330, 210, 180, 120, 30.

The upper ends are 19635, 21945, 23205, 26565, 33915, 1752465, 1915305, 1915485, 119104755, 134877435, ...

The unitary version of A294025.

No more terms below 10^9.

10^13 < a(11) <= 42229304608764255 (gap 18), while t = 220730839027951785 and t+6 are a pair with gap 6. - Giovanni Resta, May 07 2020

Examples

			Odd unitary abundant numbers are 15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, ...
Their differences are 4620, 2310, 1260, 2730, 630, 4830, 2100, 420, ...
The records of small differences are 4620, 2310, 1260, 630, 420, ...
And the corresponding terms are 15015, 19635, 21945, 25935, 33495, ...
		

Crossrefs

Cf. A129485, A294025.

Programs

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; ouaQ[n_] := OddQ[n] && usigma[n] > 2 n; s = Select[Range[100000], ouaQ]; a={}; dmin = 5000; Do[d=s[[j+1]]-s[[j]]; If[d
				

PARI

usig(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
isok(n) = (n%2) && (usig(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