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A105017 Positions of records in A064097. 9
1, 2, 3, 5, 7, 11, 19, 23, 43, 47, 94, 139, 235, 283, 517, 659, 1081, 1319, 2209, 2879, 5758, 8637, 13301, 20147, 30337, 49727, 61993, 103823, 135313, 247439, 366683, 606743, 811879, 1266767, 1739761, 2913671, 3797401, 5827343, 8288641, 16577282, 22784407, 37346483, 58003213, 81768767 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
With a(1) = 1, a(n) is the smallest number m such that the number of iterations of k -> k - k/p, p being any prime factor of k, needed to reach 1 starting at k = m is equal to n-1. (See Example section.) - Jaroslav Krizek, Feb 15 2010
a(n) =~ sqrt(e^(5n/6)). - Robert G. Wilson v, Aug 11 2022
LINKS
Hugo Pfoertner, Program
EXAMPLE
a(6)=11 because m=11 requires 6-1 = 5 iterations of r -> r - (largest divisor d < r) to reach 1 (the 5 iterations are 11-1=10, 10-5=5, 5-1=4, 4-2=2, and 2-1=1) and 11 is the smallest such number m. - Jaroslav Krizek, Feb 15 2010
MAPLE
A105017 := proc()
local maxa, a ;
maxa := -999 ;
for n from 1 do
a := A064097(n) ;
if a > maxa then
printf("%d\n", n) ;
maxa :=a ;
end if;
end do:
end proc:
A105017() ; # R. J. Mathar, Aug 07 2022
MATHEMATICA
g[n_] := Block[{p = Select[1 + Divisors@n, PrimeQ]}, n*p/(p - 1)]; f[n_] := f[n] = Block[{lst = Union@Flatten[g@# & /@ f[n - 1]]}, If[ Length@ lst > 325, lst = Take[lst, 325 (* This limit must be increased for greater n's from the start. *) ]]; lst]; f[1] = {1}; f[0] = {0}; lst = {}; Do[ AppendTo[lst, Min[ f[n]]]; f[n - 1] =., {n, 44}]; lst (* Robert G. Wilson v, Aug 11 2022 *)
PROG
(PARI) a=vectorsmall(10^7); a[1]=0;
for(n=2, #a, if(isprime(n), a[n]=1+a[n-1], f=factor(n); a[n]=a[f[1, 1]]+a[n/f[1, 1]])); \\ computes A064097
r=-oo; for(k=1, #a, if(a[k]>r, print1(k, ", "); r=a[k])); \\ Hugo Pfoertner, Mar 16 2020
CROSSREFS
Sequence in context: A228062 A332216 A059878 * A214197 A083771 A158069
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Feb 17 2006
EXTENSIONS
a(1)=1 inserted by Robert G. Wilson v, Mar 16 2020
STATUS
approved

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Last modified May 29 11:28 EDT 2024. Contains 372940 sequences. (Running on oeis4.)