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

0,3

Links

Table of n, a(n) for n=0..30.

Example

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.

Prog

(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

Crossrefs

Cf. A000079, A064097, A105017.

Sequence in context: A336631 A228129 A369695 * A171925 A186946 A057225

Adjacent sequences: A175122 A175123 A175124 * A175126 A175127 A175128

Keyword

nonn,more

Author

Jaroslav Krizek, Feb 15 2010

Extensions

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

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

Status

approved