A137809 a(0) = a(1) = 1. a(n) = a(n-1) + a(n - b(n)), where b(n) is largest prime dividing n.

1, 1, 2, 3, 5, 6, 9, 10, 19, 28, 34, 35, 63, 64, 74, 108, 182, 183, 291, 292, 400, 474, 509, 510, 984, 1384, 1448, 2432, 2906, 2907, 4291, 4292, 8583, 9092, 9275, 12181, 21273, 21274, 21566, 23014, 35195, 35196, 47377, 47378, 56470, 91665, 92175, 92176

Offset

0,3

Links

Iain Fox, Table of n, a(n) for n = 0..10000 (first 101 terms from James A. Sellers)

Formula

a(p) = a(p-1) + 1, for p prime. - Michel Marcus, Aug 11 2018

Maple

with(numtheory): a:=proc(n) option remember: if n = 0 or n = 1 then RETURN(1) fi: a(n-1) + a(n-ifactors(n)[2][nops(ifactors(n)[2])][1]): end: for i from 0 to 100 do printf(`%d, `, a(i)) od: # James A. Sellers, Feb 18 2008

Mathematica

a = {1, 1}; Do[AppendTo[a, a[[ -1]] + a[[n - FactorInteger[n][[ -1, 1]] + 1]]], {n, 2, 70}]; a (* Stefan Steinerberger, Feb 14 2008 *)

Prog

(PARI) first(n) = my(res=vector(n)); res[1]=res[2]=1; for(x=3, n, res[x] = res[x-1] + res[x-vecmax(factor(x-1)[, 1])]); res \\ Iain Fox, Aug 11 2018

Crossrefs

Cf. A006530, A137808.

Sequence in context: A018659 A018365 A018278 * A219035 A273042 A014838

Adjacent sequences: A137806 A137807 A137808 * A137810 A137811 A137812

Keyword

nonn

Author

Leroy Quet, Feb 11 2008

Extensions

More terms from Stefan Steinerberger, Feb 14 2008

Status

approved