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A189560
Least odd number k such that x' = k has n solutions, where x' is the arithmetic derivative (A003415) of x.
4
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
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 24 2011
STATUS
approved