A189560 Least odd number k such that x' = k has n solutions, where x' is the arithmetic derivative (A003415) of x.

3, 5, 21, 75, 151, 371, 671, 791, 311, 551, 1271, 1391, 1031, 2471, 2231, 4271, 1991, 3191, 5351, 7871, 7751, 7031, 8951, 8711, 11831, 5591, 19631, 10391, 15791, 20711, 30071, 17111, 30551, 27191, 40031, 31391, 52631, 49271, 35591, 42311, 50951, 92231

Offset

0,1

Comments

See A189559 for k restricted to prime numbers and A189558 for no restrictions on k.

References

See A003415.

Links

Donovan Johnson, Table of n, a(n) for n = 0..200

Formula

a(n) is the least odd k such that A099302(k) = n.

Prog

(Python)
from itertools import count
from sympy import factorint
def A189560(n):
    if n == 0:
        return 3
    mdict = {}
    for k in count(1, 2):
        c = 0
        for m in range(1, (k**2>>2)+1):
            if m not in mdict:
                mdict[m] = sum((m*e//p for p, e in factorint(m).items()))
            if mdict[m] == k:
                c += 1
            if c > n:
                break
        if c == n:
            return k # Chai Wah Wu, Sep 12 2022

Crossrefs

Cf. A003415, A189558, A189559.

Sequence in context: A056803 A071706 A196418 * A216385 A247680 A179265

Adjacent sequences: A189557 A189558 A189559 * A189561 A189562 A189563

Keyword

nonn

Author

T. D. Noe, Apr 24 2011

Status

approved