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

Author

Amiram Eldar, Oct 22 2017

Keywords

• nonn
• fini
• more

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

Examples

			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, ...
		

Links

• Carlos Rivera, Puzzle 880. Consecutive odd abundant integers

Crossrefs

Cf. A005231.

Programs

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
				

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

Extensions

a(8) from Giovanni Resta, Nov 09 2017