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A073932
Define f(n) = n - largest nontrivial divisor of n or f(n) = n-1 if n is a prime [that is, f(n) = A060681(n)]. Form a triangle in which the n-th row contains terms n, f(n), f(f(n)), ... until a 1 is reached; sequence gives triangle read by rows.
5
1, 2, 1, 3, 2, 1, 4, 2, 1, 5, 4, 2, 1, 6, 3, 2, 1, 7, 6, 3, 2, 1, 8, 4, 2, 1, 9, 6, 3, 2, 1, 10, 5, 4, 2, 1, 11, 10, 5, 4, 2, 1, 12, 6, 3, 2, 1, 13, 12, 6, 3, 2, 1, 14, 7, 6, 3, 2, 1, 15, 10, 5, 4, 2, 1, 16, 8, 4, 2, 1, 17, 16, 8, 4, 2, 1, 18, 9, 6, 3, 2, 1, 19, 18, 9, 6, 3, 2, 1, 20, 10, 5, 4, 2, 1
OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..12386 (rows 1 <= n <= 1000, flattened)
John Machacek, Egyptian Fractions and Prime Power Divisors, Journal of Integer Sequences, Vol. 21 (2018), Article 18.3.7.
EXAMPLE
Triangle begins:
1;
2, 1;
3, 2, 1;
4, 2, 1;
5, 4, 2, 1;
6, 3, 2, 1;
7, 6, 3, 2, 1;
8, 4, 2, 1;
9, 6, 3, 2, 1;
10, 5, 4, 2, 1;
MAPLE
j := 1:a[1] := 1:for i from 2 to 50 do n := i:j := j+1:a[j] := n:while(n>1) do if isprime(n) then r := n-1: else r := n-n/ifactors(n)[2][1][1]; fi; n := r:j := j+1:a[j] := n: od:od:seq(a[k], k=1..j);
MATHEMATICA
Array[If[# == 1, {1}, NestWhileList[If[PrimeQ@ #, # - 1, # - #/FactorInteger[#][[1, 1]] ] &, #, # > 1 &]] &, 20] // Flatten (* Michael De Vlieger, Apr 15 2020 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Amarnath Murthy, Aug 19 2002
EXTENSIONS
More terms from Sascha Kurz, Aug 23 2002
Offset corrected from 0 to 1 by Antti Karttunen, Aug 23 2017
STATUS
approved