A294025 Odd abundant numbers with a record small gap to the next odd abundant number.

945, 5355, 5775, 6435, 8415, 34125, 1828827, 3321765909

Offset

1,1

Comments

The corresponding gaps are 630, 420, 210, 180, 90, 30, 18, 6.

The upper ends are 1575, 5775, 5985, 6615, 8505, 34155, 1828845, 3321765915, ...

Emmanuel Vantieghem has determined that for k = 76728582876430878992529528245373 the numbers k and k+2 are abundant, so the last term of this sequence is <= k. - Giovanni Resta, Nov 09 2017

Links

Table of n, a(n) for n=1..8.

Carlos Rivera, Puzzle 880. Consecutive odd abundant integers

Example

Odd abundant numbers are 945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, ...
Their differences are 630, 630, 630, 630, 630, 630, 630, 420, 210, 450, 180, ...
The records of small differences are 630, 420, 210, 180, ...
And the corresponding terms are 945, 5355, 5775, 6435, ...

Mathematica

oaQ[n_] := OddQ[n] && DivisorSigma[1, n] > 2 n; s = Select[Range[100000], oaQ]; a={}; dmin = 1000; Do[d=s[[j+1]]-s[[j]]; If[d<dmin, AppendTo[a, s[[j]]]; dmin=d], {j, 1, Length[s]-1}]; a

Prog

(PARI) lista(nn) = {lastoa = 0; mg = oo; forstep (n=1, nn, 2, if (sigma(n) > 2*n, if (! lastoa, lastoa = n, if ((nmg = n - lastoa) < mg, mg = nmg; print1(lastoa, ", "))); lastoa = n; ); ); } \\ Michel Marcus, Nov 09 2017

Crossrefs

Cf. A005231.

Sequence in context: A188263 A188342 A109729 * A275449 A293186 A294027

Adjacent sequences: A294022 A294023 A294024 * A294026 A294027 A294028

Keyword

nonn,fini,more

Author

Amiram Eldar, Oct 22 2017

Extensions

a(8) from Giovanni Resta, Nov 09 2017

Status

approved