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