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

1,1

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

Prog

(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

Crossrefs

Cf. A003415, A086134, A235992, A327935.

Intersection of A235991 and A327863.

Sequence in context: A000053 A169871 A304144 * A079349 A355041 A212047

Adjacent sequences: A327930 A327931 A327932 * A327934 A327935 A327936

Keyword

nonn

Author

Antti Karttunen, Sep 30 2019

Status

approved