A385755 Numbers k with a unique combination of bigomega(k) and sopfr(k).
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 26, 29, 30, 31, 32, 34, 35, 36, 37, 38, 41, 43, 46, 47, 48, 53, 58, 59, 61, 62, 64, 67, 70, 71, 72, 73, 74, 79, 82, 83, 86, 89, 94, 96, 97, 101, 103, 106, 107, 109, 113, 118, 122, 127, 128, 131
Offset: 1
Keywords
Examples
All primes p are in the sequence, because they are characterized by the pair [b,s] = [bigomega=1, sopfr=p], and no other numbers have this pair.
All even semiprimes 2*p are terms, because no other number can have [b,s]=[2,p+2]. p+2 is odd, and odd semiprimes p*q would have even s.
20 with [b,s]=[3,2+2+5] and 27 with [b,s]=[3,3+3+3] are not in the sequence, because both have [b,s]=[3,9].
21 and 25 are not in the sequence, because both have [b,s]=[2,10].
36 is in the sequence as it is the only number having [4, 10]. - _David A. Corneth_, Jul 11 2025
From _Michael De Vlieger_, Jul 13 2025: (Start)
Plot a(n) at (x,y) = (A001222(a(n)), A001414(a(n))):
0 1 2 3 4 5 6 7 8 9
-----------------------------------------------------
0: 1
1:
2: 2
3: 3
4: 4
5: 5 6
6: 9 8
7: 7 10 12
8: 15 18 16
9: 14 24
10: 30 36 32
11: 11 48
12: 35 72 64
13: 13 22 96
14: 70 144 128
15: 26 192
16: 288 256
17: 17 384
18: 576 512
19: 19 34 768
... (End)
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Mathematica code.
- Michael De Vlieger, Plot a(n) at (x,y) = (A001222(a(n)), A001414(a(n))) for x <= 16 and y <= 33.
Comments