A059583 Each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(1),..,c(n) so that the reduced fraction 1 c(1) 2 c(2) 3 c(3) 5 ... c(n) prime(n) is equal to (k*m+1)/m for a positive integer m and a nonnegative integer k.

1, 2, 4, 5, 6, 6, 6, 3, 5, 6, 7, 9, 8, 7, 7, 9, 6, 8, 6, 9, 6, 8, 9, 12, 11, 5, 9, 8, 7, 7, 11, 9, 11, 11, 9, 10

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Sean A. Irvine, Java program (github)

Example

For n = 4 there are five possibilities:  1/2/3/5/7 = 1/210, 1/2*3/5*7 = 21/10, 1/2*3*5/7 = 15/14, 1/2*3*5*7 = 105/2, and 1*2/3*5*7 = 70/3. So a(4) = 5.

Prog

(Python)
from math import prod
from itertools import combinations
from sympy import prime, primerange
def a(n):
    pset = set(primerange(2, prime(n)+1))
    m, c = prod(pset), 1 # count 1/2/3/.../prime(n)
    for r in range(1, len(pset)):
        first = 1
        for dens in combinations(pset, r):
            den = prod(dens)
            num = m//den
            if dens[0] != first:
                 if den > num: break
                 first = dens[0]
            if num%den == 1: c += 1
    return c
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Sep 30 2022

Crossrefs

Sequence in context: A123124 A166236 A291768 * A086370 A083788 A058317

Adjacent sequences: A059580 A059581 A059582 * A059584 A059585 A059586

Keyword

nonn,more

Author

Naohiro Nomoto, Feb 17 2001

Extensions

More terms from Sascha Kurz, Oct 16 2001

a(34)-a(36) from Sean A. Irvine, Sep 29 2022

Definition clarified by N. J. A. Sloane, Oct 01 2022

Status

approved