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A230366
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a(n) = Sum_{k=1..floor(n/2)} (k^2 mod n).
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0
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0, 1, 1, 1, 5, 8, 7, 6, 12, 25, 22, 19, 39, 42, 35, 28, 68, 69, 76, 65, 91, 110, 92, 74, 125, 169, 144, 147, 203, 190, 186, 152, 242, 289, 245, 201, 333, 342, 286, 270, 410, 413, 430, 363, 420, 460, 423, 340, 490, 575, 578, 585, 689, 666, 605, 546, 760, 841
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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a(26) and a(27) are both squares. Conjecture: number of n such that a(n) and a(n+1) are both squares is infinite.
a(p = prime) == 0 mod p for p > 3.
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LINKS
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MATHEMATICA
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Table[Sum[Mod[k^2, n], {k, Floor[n/2]}], {n, 100}] (* T. D. Noe, Oct 22 2013 *)
Table[Sum[PowerMod[k, 2, n], {k, Floor[n/2]}], {n, 100}] (* Harvey P. Dale, Jul 03 2022 *)
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PROG
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(JavaScript)
for (i=1; i<50; i++) {
c=0;
for (j=1; j<=i/2; j++) c+=(j*j)%i;
document.write(c+", ");
}
(PARI) a(n)=sum(i=1, floor(n/2), (i*i)%n) \\ Ralf Stephan, Oct 19 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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