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
Keywords
Examples
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).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
q[n_] := SameQ @@ (FactorInteger[#][[;; , 2]]& /@ (n + {0, 1})); Select[Range[2, 600], q] -
PARI
lista(nmax) = {my(e1 = [], e2); for(n = 2, nmax, e2 = factor(n)[,2]; if(e1 == e2, print1(n-1, ", ")); e1 = e2); }
Comments