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 A000414 Numbers that are the sum of 4 nonzero squares. 50
 4, 7, 10, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS As the order of addition doesn't matter we can assume terms are in increasing order. - David A. Corneth, Aug 01 2020 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) FORMULA a(n) = n + O(log n). - Charles R Greathouse IV, Sep 03 2014 EXAMPLE From David A. Corneth, Aug 01 2020: (Start) 1608 is in the sequence as 1608 = 18^2 + 20^2 + 20^2 + 22^2. 2140 is in the sequence as 2140 = 21^2 + 21^2 + 23^2 + 27^2. 3298 is in the sequence as 3298 = 25^2 + 26^2 + 29^2 + 34^2. (End) MATHEMATICA q=16; lst={}; Do[Do[Do[Do[z=a^2+b^2+c^2+d^2; If[z<=(q^2)+3, AppendTo[lst, z]], {d, q}], {c, q}], {b, q}], {a, q}]; Union@lst (*Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *) PROG (PARI) is(n)=my(k=if(n, n/4^valuation(n, 4), 2)); k!=2 && k!=6 && k!=14 && !setsearch([0, 1, 3, 5, 9, 11, 17, 29, 41], n) \\ Charles R Greathouse IV, Sep 03 2014 (Python) limit = 10026 # 10000th term in b-file from functools import lru_cache nzs = [k*k for k in range(1, int(limit**.5)+2) if k*k + 3 <= limit] nzss = set(nzs) @lru_cache(maxsize=None) def ok(n, m): return n in nzss if m == 1 else any(ok(n-s, m-1) for s in nzs) print([n for n in range(4, limit+1) if ok(n, 4)]) # Michael S. Branicky, Apr 07 2021 (Python) from itertools import count, islice def A000414_gen(startvalue=0): # generator of terms >= startvalue return filter(lambda n:not(n in {0, 1, 3, 5, 9, 11, 17, 29, 41} or n>>((~n&n-1).bit_length()&-2) in {2, 6, 14}), count(max(startvalue, 0))) A000414_list = list(islice(A000414_gen(), 30)) # Chai Wah Wu, Jul 09 2022 CROSSREFS Cf. A000534 (complement). A###### (x, y): Numbers that are the form of x nonzero y-th powers. Cf. A000404 (2, 2), A000408 (3, 2), A000414 (4, 2), A003072 (3, 3), A003325 (3, 2), A003327 (4, 3), A003328 (5, 3), A003329 (6, 3), A003330 (7, 3), A003331 (8, 3), A003332 (9, 3), A003333 (10, 3), A003334 (11, 3), A003335 (12, 3), A003336 (2, 4), A003337 (3, 4), A003338 (4, 4), A003339 (5, 4), A003340 (6, 4), A003341 (7, 4), A003342 (8, 4), A003343 (9, 4), A003344 (10, 4), A003345 (11, 4), A003346 (12, 4), A003347 (2, 5), A003348 (3, 5), A003349 (4, 5), A003350 (5, 5), A003351 (6, 5), A003352 (7, 5), A003353 (8, 5), A003354 (9, 5), A003355 (10, 5), A003356 (11, 5), A003357 (12, 5), A003358 (2, 6), A003359 (3, 6), A003360 (4, 6), A003361 (5, 6), A003362 (6, 6), A003363 (7, 6), A003364 (8, 6), A003365 (9, 6), A003366 (10, 6), A003367 (11, 6), A003368 (12, 6), A003369 (2, 7), A003370 (3, 7), A003371 (4, 7), A003372 (5, 7), A003373 (6, 7), A003374 (7, 7), A003375 (8, 7), A003376 (9, 7), A003377 (10, 7), A003378 (11, 7), A003379 (12, 7), A003380 (2, 8), A003381 (3, 8), A003382 (4, 8), A003383 (5, 8), A003384 (6, 8), A003385 (7, 8), A003387 (9, 8), A003388 (10, 8), A003389 (11, 8), A003390 (12, 8), A003391 (2, 9), A003392 (3, 9), A003393 (4, 9), A003394 (5, 9), A003395 (6, 9), A003396 (7, 9), A003397 (8, 9), A003398 (9, 9), A003399 (10, 9), A004800 (11, 9), A004801 (12, 9), A004802 (2, 10), A004803 (3, 10), A004804 (4, 10), A004805 (5, 10), A004806 (6, 10), A004807 (7, 10), A004808 (8, 10), A004809 (9, 10), A004810 (10, 10), A004811 (11, 10), A004812 (12, 10), A004813 (2, 11), A004814 (3, 11), A004815 (4, 11), A004816 (5, 11), A004817 (6, 11), A004818 (7, 11), A004819 (8, 11), A004820 (9, 11), A004821 (10, 11), A004822 (11, 11), A004823 (12, 11), A047700 (5, 2). Sequence in context: A237707 A211642 A127958 * A025357 A222949 A144020 Adjacent sequences: A000411 A000412 A000413 * A000415 A000416 A000417 KEYWORD nonn,easy AUTHOR EXTENSIONS corrected 6/95 STATUS approved

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Last modified December 4 07:35 EST 2022. Contains 358544 sequences. (Running on oeis4.)