A143721 Aliquot sequence starting at 38.

38, 22, 14, 10, 8, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane, Nov 30 2008

Keywords

• nonn
• easy

Comments

From Michal Paulovic, Dec 31 2017: (Start)

The only integer with the sum of its proper divisors equal to 38 is 1369.

The sequence's pattern: 6+2^5, 6+2^4, 6+2^3, 6+2^2, 6+2^1, 6+2^0, 1, 0, 0, 0, ...

(End)

Part of the larger aliquot sequence: 12135617199, 5556030801, 2107460079, 1016939121, 496646799, 231221769, 85406391, 55582041, 19742503, 1794785, 366535, 107225, 25765, 5159, 1369, 38, 22, 14, 10, 8, 7, 1, 0, ..., . - Robert G. Wilson v, Mar 05 2018

Links

• Eric Weisstein's MathWorld, Aliquot Sequence

Programs

Mathematica

NestList[If[# == 0, 0, DivisorSigma[1, #] - #] &, 38, 100] (* Michael De Vlieger, Dec 31 2017 *)

PARI

x=1369; while(x,x=sigma(x)-x;if(x,print1(x ", "),print1(x ", " x ", " x ", ..."))) \\ Michal Paulovic, Dec 31 2017

Formula

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

From Iain Fox, Dec 31 2017: (Start)

G.f.: 38 + 22*x + 14*x^2 + 10*x^3 + 8*x^4 + 7*x^5 + x^6.

E.g.f.: (27360 + 15840*x + 5040*x^2 + 1200*x^3 + 240*x^4 + 42*x^5 + x^6)/720.

(End)