A358148 Aliquot sequence starting at 326.

326, 166, 86, 46, 26, 16, 15, 9, 4, 3, 1, 0

Offset: 0

Author

Michal Paulovic, Oct 31 2022

Keywords

• nonn
• easy
• fini
• full

Comments

Starting with untouchable number 326, this sequence is not a part of any larger aliquot sequence.

The sequence's pattern: 2^5*10+6, 2^4*10+6, 2^3*10+6, 2^2*10+6, 2^1*10+6, 2^0*10+6, 2^4-1, 2^3+1, 2^2-0, 2^1+1, 2^0-1.

Crossrefs

Includes A143759.

Programs

Maple

with(numtheory): 326; while % > 0 do sigma(%)-% end do;

Mathematica

NestList[If[# == 0, 0, DivisorSigma[1, #] - #] &, 326, 11]

PARI

x=326; print1(x ", "); while(x, x=sigma(x)-x; if(x, print1(x ", "), print1(x)))

Formula

a(n+1) = A001065(a(n)).

G.f.: 326 + 166*x + 86*x^2 + 46*x^3 + 26*x^4 + 16*x^5 + 15*x^6 + 9*x^7 + 4*x^8 + 3*x^9 + x^10.

E.g.f.: (1182988800 + 602380800*x + 156038400*x^2 + 27820800*x^3 + 3931200*x^4 + 483840*x^5 + 75600*x^6 + 6480*x^7 + 360*x^8 + 30*x^9 + x^10)/3628800.