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A384992
Positive numbers k whose prime factors together with their exponents are distinct.
0
1, 2, 3, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 32, 37, 40, 41, 43, 45, 47, 48, 49, 53, 56, 59, 61, 63, 64, 67, 71, 73, 75, 79, 80, 81, 83, 88, 89, 96, 97, 99, 101, 103, 104, 107, 109, 112, 113, 117, 121, 125, 127, 128, 131, 136, 137, 139, 147, 149
OFFSET
1,2
EXAMPLE
1 is a term because it has no prime factors and thus no duplicates.
96 is a term because 96 = 2^5 * 3^1 and 1, 2, 3 and 5 are distinct.
24 is not a term because 24 = 2^3 * 3^1 where the number 3 occurs twice.
MATHEMATICA
q[k_] := UnsameQ @@ Flatten[FactorInteger[k]]; Join[{1}, Select[Range[2, 150], q]] (* Amiram Eldar, Sep 08 2025 *)
PROG
(Python)
from sympy import factorint
def ok(n):
f = factorint(n)
return len(L:=list(f.keys())+list(f.values())) == len(set(L))
print([k for k in range(1, 150) if ok(k)]) # Michael S. Branicky, Sep 07 2025
(PARI) isok(k) = my(f=factor(k), v=concat(f[, 1], f[, 2])); #v == #Set(v); \\ Michel Marcus, Sep 08 2025
CROSSREFS
Supersequence of A000040.
Subsequence of A130091.
Sequence in context: A063743 A353968 A144100 * A359059 A328320 A086539
KEYWORD
easy,nonn
AUTHOR
Kalle Siukola, Sep 07 2025
STATUS
approved