A334099 - OEIS

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

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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