OFFSET
1,1
COMMENTS
The ordered prime signature of a number n is the list of exponents of the distinct prime factors in the prime factorization of n, in the order of the prime factors (A124010).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
14 is a term since 14 = 2^1 * 7^1 and 15 = 3^1 * 5^1 have the same ordered prime signature, (1, 1).
44 is a term since 44 = 2^2 * 11^1 and 45 = 3^2 * 5^1 have the same ordered prime signature, (2, 1).
75 is a term of A052213 but not a term of this sequence, since 75 = 3^1 * 5^2 and 76 = 2^2 * 19^1 have different ordered prime signatures, (1, 2) and (2, 1).
MATHEMATICA
q[n_] := SameQ @@ (FactorInteger[#][[;; , 2]]& /@ (n + {0, 1})); Select[Range[2, 600], q]
PROG
(PARI) lista(nmax) = {my(e1 = [], e2); for(n = 2, nmax, e2 = factor(n)[, 2]; if(e1 == e2, print1(n-1, ", ")); e1 = e2); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 13 2023
STATUS
approved