A359745 Numbers k such that k and k+1 have the same ordered prime signature.

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

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

Subsequence of A052213.

A359746 is a subsequence.

Cf. A124010.

Sequence in context: A140578 A052213 A280074 * A086263 A355709 A335071

Adjacent sequences: A359742 A359743 A359744 * A359746 A359747 A359748

Keyword

nonn

Author

Amiram Eldar, Jan 13 2023

Status

approved