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.

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

Author

Amarnath Murthy, Aug 19 2002

Keywords

• nonn
• tabf

Examples

			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;
		

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.

Crossrefs

Cf. A032742, A060681, A073933, A073934, A073935.

Programs

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 *)

Extensions

More terms from Sascha Kurz, Aug 23 2002

Offset corrected from 0 to 1 by Antti Karttunen, Aug 23 2017