OFFSET
0,3
COMMENTS
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 0..10000
EXAMPLE
The terms together with their prime indices of binary indices begin:
0: {}
1: {{}}
2: {{1}}
3: {{},{1}}
6: {{1},{2}}
7: {{},{1},{2}}
8: {{1,1}}
9: {{},{1,1}}
10: {{1},{1,1}}
11: {{},{1},{1,1}}
12: {{2},{1,1}}
13: {{},{2},{1,1}}
14: {{1},{2},{1,1}}
15: {{},{1},{2},{1,1}}
22: {{1},{2},{3}}
23: {{},{1},{2},{3}}
28: {{2},{1,1},{3}}
29: {{},{2},{1,1},{3}}
30: {{1},{2},{1,1},{3}}
31: {{},{1},{2},{1,1},{3}}
32: {{1,2}}
MATHEMATICA
normQ[m_]:=m=={}||Union[m]==Range[Max[m]];
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], normQ[Join@@prix/@bpe[#]]&]
PROG
(Python)
from itertools import count, islice
from sympy import sieve, factorint
def a_gen():
for n in count(0):
s = set()
b = [(i+1) for i, x in enumerate(bin(n)[2:][::-1]) if x =='1']
for i in b:
p = factorint(i)
for j in p:
s.add(sieve.search(j)[0])
x = sorted(s)
y = len(x)
if sum(x) == (y*(y+1))//2:
yield n
A371292_list = list(islice(a_gen(), 65)) # John Tyler Rascoe, May 21 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Mar 27 2024
STATUS
approved