The On-Line Encyclopedia of Integer Sequences (OEIS)

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A164098

Numbers of the form n * (k_1^2 + k_2^2 + ... + k_n^2).
(history; published version)

#8 by Joerg Arndt at Tue Sep 12 02:49:16 EDT 2017

STATUS

proposed

approved

#7 by Michel Marcus at Mon Sep 11 17:14:45 EDT 2017

STATUS

editing

proposed

#6 by Michel Marcus at Mon Sep 11 17:14:31 EDT 2017

PROG

From Franklin T. Adams-Watters, Aug 29 2009: (Start)

(PARI) issumsqs(n, k) = if(n<=0||k<=0, return(k==0&&n==0)); forstep(j=sqrtint(n), max(sqrtint(n\k), 1), -1, if(issumsqs(n-j^2, k-1), return(1))); 0

for(n=1, 200, if(isa(n), print1(n", "))) (End)\\ _Franklin T. Adams-Watters_, Aug 29 2009

STATUS

proposed

editing

#5 by Wesley Ivan Hurt at Mon Sep 11 16:53:32 EDT 2017

STATUS

editing

proposed

#4 by Wesley Ivan Hurt at Mon Sep 11 16:52:54 EDT 2017

NAME

Numbers of the form n * (k_1^2 + k_2^2 + ... + k_n^2 ).

COMMENTS

Contribution from _From _Franklin T. Adams-Watters_, Aug 29 2009: (Start)

EXAMPLE

34 = 2*(4^2 + 1^2), 42 = 3*(3^2 + 2^2 + 1^2), thus 34 and 42 are in the sequence.

PROG

Contribution from _From _Franklin T. Adams-Watters_, Aug 29 2009: (Start)

CROSSREFS

Cf. A000290, A000404, A000408, A000414, A047700, A111178. [From Franklin T. Adams-Watters, Aug 29 2009]

STATUS

approved

editing

#3 by N. J. A. Sloane at Tue May 20 14:52:33 EDT 2014

AUTHOR

_Jonas Wallgren (jonwa(AT)ida.liu.se), _, Aug 10 2009, Aug 17 2009

Discussion

Tue May 20

14:52

OEIS Server: https://oeis.org/edit/global/2219

#2 by Russ Cox at Fri Mar 30 17:35:23 EDT 2012

COMMENTS

Contribution from _Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Aug 29 2009: (Start)

PROG

Contribution from _Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Aug 29 2009: (Start)

CROSSREFS

Cf. A000290,A000404,A000408,A000414,A047700,A111178. [From _Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Aug 29 2009]

EXTENSIONS

More terms from _Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Aug 29 2009

Discussion

Fri Mar 30

17:35

OEIS Server: https://oeis.org/edit/global/165

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Numbers of the form n*(k_1^2 + k_2^2 + ... + k_n^2 )

DATA

1, 4, 9, 10, 16, 18, 20, 25, 26, 27, 28, 33, 34, 36, 40, 42, 48, 49, 50, 51, 52, 54, 55, 57, 58, 60, 63, 64, 65, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 95, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 120, 121, 122, 123, 124, 125

OFFSET

1,2

COMMENTS

Contribution from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2009: (Start)

The k_i must all be positive integers.

Note that every integer > 33 is the sum of 5 positive squares, and for n > 5, every integer > n+13 is the sum of n positive squares. (End)

EXAMPLE

34=2*(4^2 + 1^2), 42=3*(3^2 + 2^2 + 1^2), thus 34 and 42 are in the sequence.

PROG

Contribution from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2009: (Start)

(PARI) issumsqs(n, k)=if(n<=0||k<=0, return(k==0&&n==0)); forstep(j=sqrtint(n), max(sqrtint(n\k), 1), -1, if(issumsqs(n-j^2, k-1), return(1))); 0

isa(n)=local(ds); ds=divisors(n); for(k=1, (#ds+1)\2, if(issumsqs(n\ds[k], ds[k]), return(1))); 0

for(n=1, 200, if(isa(n), print1(n", "))) (End)

CROSSREFS

Cf. A000290,A000404,A000408,A000414,A047700,A111178. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2009]

KEYWORD

nonn

AUTHOR

Jonas Wallgren (jonwa(AT)ida.liu.se), Aug 10 2009, Aug 17 2009

EXTENSIONS

More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2009

STATUS

approved