A091293 - OEIS

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A091293

a(n) is the smallest x for which the following quotient is an integer: (sigma(x) + ... + sigma(x+n-1))/sigma(x+(x+1)+ ... + (x+n-1)), i.e., sum(sigma(j))/sigma(sum(j)) for n terms summed up was integer.

1, 1, 424, 7, 13980, 2, 805675056, 15662957033, 7, 42, 48957 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,3`
	COMMENTS	`Some other values: a(15)=298, a(19)=97.` `a(12) > 8*10^10. - Giovanni Resta, May 07 2017`
	LINKS	`Table of n, a(n) for n=1..11.`
	EXAMPLE	`n=6: sigma(2) + sigma(3) + ... + sigma(7) = 3 + 4 + 7 + 6 + 12 + 8 = 40 = sigma(2 + 3 + ... + 7) = sigma(27) = 1 + 3 + 9 + 27 = 40; quotient = 1.`
	MATHEMATICA	`g[x_, k_] := Apply[Plus, Table[sg[x+j], j, 0, k-1}]]/ sg[Apply[Plus, Table[x+j, j, 0, k-1}]]] Table[fla=1; Do[s=g[n, h]; If[IntegerQ[s]&&Equal[fla, 1], Print[{n, h}]; fla=0], {n, 1, 10000000}], {h, 1, 6}]`
	CROSSREFS	`Cf. A000203, A091287-A091293.` `Sequence in context: A238174 A251013 A230678 * A114808 A134218 A246733` `Adjacent sequences: A091290 A091291 A091292 * A091294 A091295 A091296`
	KEYWORD	`hard,nonn`
	AUTHOR	`Labos Elemer, Feb 17 2004`
	EXTENSIONS	`a(7)-a(11) from Giovanni Resta, May 07 2017`
	STATUS	`approved`

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Last modified May 22 17:42 EDT 2022. Contains 353957 sequences. (Running on oeis4.)