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A327935
Numbers for which the smallest prime factor of their arithmetic derivative is 5.
4
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
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
Subsequence of A235991, and also of A327865.
Sequence in context: A145002 A043076 A154651 * A079910 A103768 A325947
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 30 2019
STATUS
approved