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

1,1

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

Links

Table of n, a(n) for n=1..10.

Example

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, ...

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<dmin, AppendTo[a, s[[j]]]; dmin=d], {j, 1, Length[s]-1}]; a

Prog

(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

Crossrefs

Cf. A129485, A294025.

Sequence in context: A379031 A249263 A335052 * A133778 A200090 A147578

Adjacent sequences: A294023 A294024 A294025 * A294027 A294028 A294029

Keyword

nonn,fini,more

Author

Amiram Eldar, Oct 22 2017

Status

approved