The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A348169 Positive integers which can be represented as A*(x^2 + y^2 + z^2) = B*(x*y + x*z + y*z) with positive integers x, y, z, A, B and gcd(A,B)=1. 1
 3, 12, 18, 27, 30, 42, 48, 72, 75, 77, 98, 108, 120, 147, 154, 162, 168, 192, 243, 255, 260, 264, 270, 272, 273, 285, 288, 297, 300, 308, 338, 363, 378, 392, 432, 450, 462, 480, 490, 494, 507, 510, 513, 588, 616, 630, 648, 672, 675, 693, 702, 714, 722, 750, 754, 768, 798 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence represents a generalization of cases A033428 (k=1), A347960 (k=2), A347969 (k=5) with all possible k given by A331605. Instead of integer k, it utilizes the ratio B/A. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 Alexander Kritov, Source code EXAMPLE a(6)=42: the quintuple (x,y,z) A,B is 1,2,4 (2,3) because 42 = 2*(1^2 + 2^2 + 4^2) = 3*(1*4 + 1*2 + 2*4). a(n) (x,y,z) A, B 3 (1,1,1) 1, 1 12 (2,2,2) 1, 1 18 (1,1,4) 1, 2 27 (3,3,3) 1, 1 30 (1,1,2) 5, 6 42 (1,2,4) 2, 3 48 (4,4,4) 1, 1 72 (1,2,2) 8, 9 [also (2,2,8) 1, 2] 75 (5,5,5) 1, 1 77 (1,1,3) 7, 11 98 (1,4,9) 1, 2 108 (6,6,6) 1, 1 120 (2,2,4) 5, 6 147 (7,7,7) 1, 1 154 (1,2,3) 11, 14 162 (3,3,12) 1, 2 168 (2,4,8) 2, 3 192 (8,8,8) 1, 1 243 (9,9,9) 1, 1 255 (1,1,7) 5, 17 260 (2,5,6) 4, 5 264 (1,4,4) 8, 11 270 (2,5,5) 5, 6 272 (2,2,3) 16, 17 288 (4,4,2) 8, 9 [also (4,4,16) 1, 2] PROG (C) See links. (Python) from itertools import islice, count from math import gcd from sympy import divisors, integer_nthroot def A348169(): # generator of terms for n in count(1): for d in divisors(n, generator=False): x, x2 = 1, 1 while 3*x2 <= d: y, y2 = x, x2 z2 = d-x2-y2 while z2 >= y2: z, w = integer_nthroot(z2, 2) if w: A = n//d B, u = divmod(n, x*(y+z)+y*z) if u == 0 and gcd(A, B) == 1: yield n break y += 1 y2 += 2*y-1 z2 -= 2*y-1 else: x += 1 x2 += 2*x-1 continue break else: continue break A348169_list = list(islice(A348169(), 57)) # Chai Wah Wu, Nov 26 2021 CROSSREFS Cf. A331605, A347969, A347960. The sequence contains A033428 (A=B=1), A347969 (B=2*A), A347960 (B=5*A). Sequence in context: A239052 A063229 A061564 * A342785 A166038 A052637 Adjacent sequences: A348166 A348167 A348168 * A348170 A348171 A348172 KEYWORD nonn AUTHOR Alexander Kritov, Oct 04 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 15 02:01 EDT 2024. Contains 371667 sequences. (Running on oeis4.)