A175125 a(n) is the number of numbers m such that the number of iterations of r -> r - (largest divisor d < r) needed to reach 1 starting at r = m is equal to n.

1, 1, 2, 3, 5, 9, 13, 23, 36, 65, 100, 175, 275, 468, 760, 1266, 2077, 3454, 5690, 9449, 15547, 25709, 42459, 70181, 115947, 191509, 316570, 523087, 864406, 1428174, 2359266

Offset: 0

Author

Jaroslav Krizek, Feb 15 2010

Keywords

• nonn
• more

Examples

			Example (a(4)=5): There are five numbers (7,9,10,12,16) with 4 steps of defined iteration: 7-1=6, 6-3=3, 3-1=2, 2-1=1; 9-3=6, 6-3=3, 3-1=2, 2-1=1; 10-5=5, 5-1=4, 4-2=2, 2-1=1; 12-6=6, 6-3=3, 3-1=2, 2-1=1; 16-8=8, 8-4=4, 4-2=2, 2-1=1.
		

Crossrefs

Cf. A000079, A064097, A105017.

Programs

PARI

a064097(n)={my(k=1,d=divisors(n),r=n-d[#d-1]);while(r>1,d=divisors(r);r-=d[#d-1];k++);k};
my(c=vector(50));for(k=2,2^20,j=a064097(k);c[j]++);concat([1],c[1..20]) \\ Hugo Pfoertner, Mar 23 2020

Extensions

a(8)-a(27) from Hugo Pfoertner, Mar 23 2020

a(28)-a(30) from Robert G. Wilson v, Apr 05 2020