A327935 Numbers for which the smallest prime factor of their arithmetic derivative is 5.

6, 46, 75, 106, 150, 166, 175, 226, 250, 266, 325, 346, 350, 406, 429, 466, 475, 526, 546, 550, 586, 646, 650, 682, 706, 750, 759, 766, 775, 826, 847, 850, 886, 925, 950, 966, 1006, 1050, 1075, 1083, 1106, 1126, 1150, 1186, 1209, 1246, 1250, 1254, 1306, 1326, 1342, 1366, 1406, 1419, 1421, 1450, 1486, 1525, 1526, 1546

Offset

1,1

Comments

Numbers n for which A086134(n) = 5.

Numbers whose arithmetic derivative is an odd multiple of five, but is not a multiple of three.

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]); };
isA327935(n) = (5==A086134(n));
(Python)
from itertools import count, islice
from sympy import factorint
def A327935_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 m%3 and not m%5, count(max(startvalue, 2)))
A327935_list = list(islice(A327935_gen(), 40)) # Chai Wah Wu, Nov 04 2022

Crossrefs

Cf. A003415, A086134, A235992, A327933.

Subsequence of A235991, and also of A327865.

Sequence in context: A145002 A043076 A154651 * A079910 A103768 A325947

Adjacent sequences: A327932 A327933 A327934 * A327936 A327937 A327938

Keyword

nonn

Author

Antti Karttunen, Sep 30 2019

Status

approved