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A359745
Numbers k such that k and k+1 have the same ordered prime signature.
2
2, 14, 21, 33, 34, 38, 44, 57, 85, 86, 93, 94, 116, 118, 122, 133, 135, 141, 142, 145, 158, 171, 177, 201, 202, 205, 213, 214, 217, 218, 230, 253, 285, 296, 298, 301, 302, 326, 332, 334, 381, 387, 393, 394, 429, 434, 445, 446, 453, 481, 501, 514, 526, 537, 542
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
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
Subsequence of A052213.
A359746 is a subsequence.
Cf. A124010.
Sequence in context: A140578 A052213 A280074 * A086263 A355709 A335071
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 13 2023
STATUS
approved