The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A018820 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A018820

Numbers k that are the sum of m nonzero squares for all 1 <= m <= k - 14.
(history; published version)

#22 by Susanna Cuyler at Fri Feb 12 17:51:09 EST 2021

STATUS

proposed

approved

#21 by Jianing Song at Tue Feb 09 22:22:20 EST 2021

STATUS

editing

proposed

#20 by Jianing Song at Tue Feb 09 22:22:10 EST 2021

PROG

(PARI) isA018820(n) = issquare(n) && isA341329(sqrtint(n)) \\ Jianing Song, Feb 09 2021, see program of A341329 for its program

STATUS

proposed

editing

#19 by Jianing Song at Tue Feb 09 19:12:49 EST 2021

STATUS

editing

proposed

#18 by Jianing Song at Tue Feb 09 19:12:45 EST 2021

COMMENTS

Note that k^2 is never the sum of k^2 - 13 positive squares. - Jianing Song, Feb 09 2021

#17 by Jianing Song at Tue Feb 09 19:11:21 EST 2021

COMMENTS

Note that k^2 is never the sum of k^2 - 13 positive squares. - Jianing Song, Feb 09 2021

FORMULA

a(n) = A341329(n)^2. - Jianing Song, Feb 09 2021

EXAMPLE

169 is a term: 169 = 13^2 = 5^2 + 12^2 = 3^2 + 4^2 + 12^2 = 11^2 + 4^2 + 4^2 + 4^2 = 6^2 + 6^2 + 6^2 + 6^2 + 5^2 = 6^2 + 6^2 + 6^2 + 6^2 + 4^2 + 3^2 = ... = 3^2 + 2^2 + 2^2 + 1^2 + 1^2 + ... + 1^2 (sum of 155 positive squares, with 152 (1^2)'s), but 169 cannot be represented as the sum of 156 positive squares. - Jianing Song, Feb 09 2021

PROG

(PARI) isA018820(n) = issquare(n) && isA341329(sqrtint(n)) \\ Jianing Song, Feb 09 2021, see program of A341329

CROSSREFS

Cf. A000290, A000404, A000408, A309778, A341329.

STATUS

approved

editing

#16 by Joerg Arndt at Tue Feb 09 09:55:27 EST 2021

STATUS

reviewed

approved

#15 by Hugo Pfoertner at Tue Feb 09 08:47:32 EST 2021

STATUS

proposed

reviewed

#14 by Jianing Song at Tue Feb 09 08:30:05 EST 2021

STATUS

editing

proposed

#13 by Jianing Song at Tue Feb 09 08:29:47 EST 2021

NAME

n is Numbers k that are the sum of k m nonzero squares for all 1 <= m <= k <= n- 14.

COMMENTS

A square nk^2 is the sum of k m positive squares for all 1 <= m <= k <= n^2 - 14 iff nk^2 is the sum of 2 and 3 positive squares (see A309778 and proof in Kuczma). - Bernard Schott, Aug 17 2019

STATUS

proposed

editing

Discussion

Tue Feb 09

08:30

Jianing Song: Agree. Edited.