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A000414 Numbers that are the sum of 4 nonzero squares. 47
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)

Index entries for sequences related to sums of squares

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

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

N. J. A. Sloane and J. H. Conway

EXTENSIONS

corrected 6/95

STATUS

approved

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Last modified February 27 05:37 EST 2021. Contains 341649 sequences. (Running on oeis4.)