A323073 Number of iterations of A049820(x) = x - A000005(x) needed to reach either zero or such x that x and A049820(x) are coprime, when starting from x = n.

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

Offset

0,7

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..110880

Formula

a(0) = 0; for n > 0, if A009191(n) == 1, a(n) = 0, otherwise a(n) = 1 + a(n-A000005(n)).

a(n) <= A155043(n).

Prog

(PARI) A323073(n) = if(!n, 0, my(nn=(n-numdiv(n))); if(1==gcd(n, nn), 0, 1+A323073(nn)));
(PARI) A323073(n) = if(!n, 0, for(j=0, oo, my(nn=(n-numdiv(n))); if((0==nn)||(1==gcd(n, nn)), return(j+(2==n)), n = nn)));

Crossrefs

Cf. A000005, A009191, A049820, A155043, A259934, A286540, A320009, A322974, A322987, A322996.

Cf. A046642 (positions of zeros after the initial a(0)=0).

Sequence in context: A242379 A103438 A291556 * A167279 A068920 A363882

Adjacent sequences: A323070 A323071 A323072 * A323074 A323075 A323076

Keyword

nonn

Author

Antti Karttunen, Jan 05 2019

Status

approved