A327933 Numbers such that the smallest prime factor of their arithmetic derivative is 3.

14, 18, 26, 27, 38, 45, 50, 54, 62, 63, 74, 86, 90, 99, 110, 117, 122, 125, 126, 134, 146, 153, 158, 162, 170, 171, 194, 198, 206, 207, 218, 230, 234, 242, 243, 254, 261, 270, 275, 278, 279, 290, 302, 306, 314, 326, 333, 342, 343, 362, 369, 374, 378, 386, 387, 398, 405, 410, 414, 422, 423, 425, 446, 450, 458, 470

Offset: 1

Author

Antti Karttunen, Sep 30 2019

Keywords

• nonn

Comments

Numbers n for which A086134(n) = 3.

Numbers whose arithmetic derivative is an odd multiple of 3.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A086134, A235992, A327935.

Intersection of A235991 and A327863.

Programs

PARI

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A086134(n) = { my(d=A003415(n)); if(d<=1,0,factor(d)[1, 1]); };
isA327933(n) = (3==A086134(n));

Python

from itertools import count, islice
from sympy import factorint
def A327933_gen(startvalue=2): # generator of terms >= startvalue
    return filter(lambda n: (m:=sum((n*e//p for p,e in factorint(n).items())))&1 and not m%3, count(max(startvalue,2)))
A327933_list = list(islice(A327933_gen(),40)) # Chai Wah Wu, Nov 04 2022