OFFSET
0,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..73
FORMULA
a(n) = A143658(n)+1 for n > 1. - Chai Wah Wu, Aug 26 2024
EXAMPLE
The squarefree numbers A005117(a(n)) together with their binary expansions and binary indices begin:
1: 1 ~ {1}
2: 10 ~ {2}
5: 101 ~ {1,3}
10: 1010 ~ {2,4}
17: 10001 ~ {1,5}
33: 100001 ~ {1,6}
65: 1000001 ~ {1,7}
129: 10000001 ~ {1,8}
257: 100000001 ~ {1,9}
514: 1000000010 ~ {2,10}
1027: 10000000011 ~ {1,2,11}
2049: 100000000001 ~ {1,12}
4097: 1000000000001 ~ {1,13}
8193: 10000000000001 ~ {1,14}
16385: 100000000000001 ~ {1,15}
32770: 1000000000000010 ~ {2,16}
65537: 10000000000000001 ~ {1,17}
131073: 100000000000000001 ~ {1,18}
MATHEMATICA
nn=1000;
ssnm[y_]:=Max@@NestWhile[Most, y, Union[#]!=Range[Max@@#]&];
dcs=IntegerLength[Select[Range[nn], SquareFreeQ], 2];
Table[Position[dcs, i][[1, 1]], {i, ssnm[dcs]}]
PROG
(Python)
from itertools import count
from math import isqrt
from sympy import mobius, factorint
def A372540(n): return next(sum(mobius(a)*(k//a**2) for a in range(1, isqrt(k)+1)) for k in count(1<<n) if max(factorint(k).values(), default=0)==1) if n else 1 # Chai Wah Wu, May 12 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, May 10 2024
EXTENSIONS
a(24)-a(34) from Chai Wah Wu, May 12 2024
STATUS
approved