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

0,1

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

References

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

Links

Table of n, a(n) for n=0..51.

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).

Formula

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

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

Example

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

Mathematica

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

Crossrefs

Cf. A001065, A063990.

Sequence in context: A371808 A371806 A217160 * A274116 A121507 A255215

Adjacent sequences: A203774 A203775 A203776 * A203778 A203779 A203780

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Jan 05 2012

Status

approved