A322987 Number of iterations of A049820(x) = x - A000005(x) needed to reach a square, when starting from x = n.

0, 0, 1, 1, 0, 2, 2, 3, 1, 0, 3, 1, 3, 2, 4, 2, 0, 3, 4, 4, 5, 4, 5, 5, 1, 0, 6, 6, 6, 7, 6, 8, 7, 8, 7, 9, 0, 10, 8, 10, 8, 11, 8, 12, 9, 11, 9, 12, 9, 0, 10, 13, 10, 14, 10, 14, 10, 15, 11, 16, 10, 17, 12, 16, 0, 18, 12, 19, 13, 19, 13, 20, 11, 21, 14, 20, 14, 22, 14, 23, 14, 0, 15, 1, 12, 1, 16, 2, 15, 3, 15, 3, 17, 4, 16, 4, 13, 5, 18, 5, 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. A000290, A010052, A049820, A155043, A259934, A262514, A262680, A322996, A323073.

Programs

PARI

A322987(n) = if(issquare(n),0,1+A322987(n-numdiv(n)));

PARI

A322987(n) = { for(j=0,oo,if(issquare(n),return(j)); n -= numdiv(n)); };

Formula

If A010052(n) == 1 [when n is in A000290], then a(n) = 0, otherwise a(n) = 1+a(A049820(n)).

a(n) <= A155043(n).

For n >= 83, a(2*n) = A322996(2*n)-1. [Note that 2*83 = 166 > 144 = A262514(2).]