A203777 Aliquot sequence starting at 220.

220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284, 220, 284

Offset: 0

Author

Arkadiusz Wesolowski, Jan 05 2012

Keywords

• nonn
• easy

Comments

A period 2 sequence.

The sum of the proper divisors of 220 is 284 and the sum of the proper divisors of 284 is 220.

Sierpiński's book has typos for n = 1 and 3 (280 instead of 284).

Also continued fraction expansion of (7810+sqrt(61000005))/71. - Bruno Berselli, Jan 18 2012

Examples

			a(0) = 220, a(1) = sigma(220) - 220 = 284.
		

References

• Wacław Sierpiński, Czym sie zajmuje teoria liczb. Warsaw: PW "Wiedza Powszechna", 1957, p. 138.

Links

• J. Perrott, Sur une proposition empirique énoncée au Bulletin, Bulletin de la S. M. F., tome 17 (1889), pp. 155-156.
• Wikipedia, Aliquot sequence.
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A001065, A063990.

Programs

Mathematica

RecurrenceTable[{a[n] == DivisorSigma[1, a[n - 1]] - a[n - 1], a[0] == 220}, a, {n, 51}]

Formula

a(2*n) = 220, a(2*n+1) = 284.

a(n+1) = A001065(a(n)). - R. J. Mathar, Oct 11 2017