A322996 Number of iterations of A049820(x) = x - A000005(x) needed to reach an odd number or zero, when starting from x = n.

0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 3, 0, 4, 0, 1, 0, 4, 0, 5, 0, 5, 0, 2, 0, 6, 0, 6, 0, 6, 0, 7, 0, 7, 0, 1, 0, 8, 0, 8, 0, 8, 0, 9, 0, 9, 0, 9, 0, 10, 0, 10, 0, 10, 0, 10, 0, 11, 0, 10, 0, 12, 0, 1, 0, 12, 0, 13, 0, 13, 0, 11, 0, 14, 0, 14, 0, 14, 0, 14, 0, 15, 0, 12, 0, 16, 0, 15, 0, 15, 0, 17, 0, 16, 0, 13, 0, 18, 0, 1, 0, 17, 0, 14, 0

Offset: 0

Author

Antti Karttunen, Jan 05 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..110880

Crossrefs

Cf. A000005, A049820, A155043, A259934, A322987, A322997 (bisection), A323073.

Cf. also A322983.

Programs

Mathematica

A322996[n_] := A322996[n] = If[n == 0 || OddQ[n], 0, 1 + A322996[n - DivisorSigma[0, n]]];
Array[A322996, 100, 0] (* Paolo Xausa, Jan 15 2025 *)

PARI

A322996(n) = if((!n)||(n%2),0,1+A322996(n-numdiv(n)));

PARI

A322996(n) = { for(j=0,oo,if((!n)||(n%2),return(j)); n -= numdiv(n)); };

Formula

a(0) = 0; for n >= 1, for n odd, a(n) = 0, and for n even, a(n) = 1 + a(n-A000005(n)).

a(n) <= A155043(n).

For n >= 83, a(2*n) = 1+A322987(2*n).