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

Author

Antti Karttunen, Sep 30 2019

Keywords

• nonn

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

Crossrefs

Cf. A003415, A086134, A235992, A327933.

Subsequence of A235991, and also of A327865.

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]); };
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