A334099 The least k for which A329697(k) = n; Position of first occurrence of n (and also records) in A329697.

1, 3, 7, 19, 43, 127, 283, 659, 1319, 3957, 9227, 21599, 50123, 129263, 258527, 775581, 1551163, 4340087, 9750239, 27353747, 65148847, 156067127, 340997113, 955523423

Offset

0,2

Comments

Note that although most of the terms after 1 are primes, we also have a few composites: a(9) = a(1)*a(8) = 3*1319 = 3957, a(15) = a(1)*a(14) = 3*258527 = 775581, a(22) = a(8)*a(14) = 340997113.

a(n) <= 3^n and in particular, a(n+1) <= 3*a(n), n > 0 and more generally a(n + m) <= a(n) * a(m) where m, n >= 0. - David A. Corneth, Apr 15 2020

The above follows because A329697 is totally additive.

Links

Table of n, a(n) for n=0..23.

Formula

For all n >= 0, A329697(a(n)) = n.

Mathematica

With[{s = Array[Length@ NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, 10^6]}, {1}~Join~Array[FirstPosition[s, #][[1]] &, Max@ s]] (* Michael De Vlieger, Apr 30 2020 *)

Prog

(PARI)
A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));
m=-1; k=0; for(n=1, 2^32, t=A329697(n); if(t>m, m=t; write("b334099.txt", k, " ", n); k++));

Crossrefs

The leftmost column of A334100.

Cf. A329697 (a left inverse).

Cf. A067513.

Cf. A007755, A105017, and also A329662 (analogous sequence when using the map k -> k + k/p).

Sequence in context: A055622 A075900 A176500 * A136041 A146685 A146653

Adjacent sequences: A334096 A334097 A334098 * A334100 A334101 A334102

Keyword

nonn,more

Author

Antti Karttunen, Apr 14 2020

Status

approved