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A276318 Least number k such that sigma(Sum_{j=0..n}{k-j}) = sigma(Sum_{j=0..n}{k+j}). 3
1, 17, 89, 79, 321, 49, 23, 20, 139, 87, 26, 48, 41, 56, 75, 88, 38, 81, 49, 134, 196, 78, 68, 114, 155, 65, 552, 111, 80, 349, 103, 104, 142, 192, 110, 342, 123, 359, 395, 249, 83, 349, 101, 74, 481, 292, 219, 1110, 189, 128, 309, 243, 224, 629, 356, 170, 208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Paolo P. Lava, Table of n, a(n) for n = 0..1000

FORMULA

Solutions of the equation  sigma((n+1)*(2*k-n)/2) = sigma((n+1)*(2*k+n)/2).

EXAMPLE

a(3) = 79 because sigma(76+77+78+79) = sigma(79+80+81+82) = 576.

MAPLE

with(numtheory): P:= proc(q) local k, n; print(1);

for n from 1 to q do for k from n to q do

if sigma((n+1)*(2*k-n)/2)=sigma((n+1)*(2*k+n)/2)

then print(k); break; fi; od; od; end: P(10^9);

MATHEMATICA

Table[k = n; While[DivisorSigma[1, Sum[k - j, {j, 0, n}]] != DivisorSigma[1, Sum[k + j, {j, 0, n}]], k++]; k, {n, 0, 56}] (* Michael De Vlieger, Aug 30 2016 *)

PROG

(PARI) a(n) = {if (n==0, k = 1, k = n); while (sigma((n+1)*(2*k-n)/2) != sigma((n+1)*(2*k+n)/2), k++); k; }

CROSSREFS

Cf. A000203, A276319, A276320.

Sequence in context: A271567 A231704 A033654 * A282378 A248400 A139947

Adjacent sequences:  A276315 A276316 A276317 * A276319 A276320 A276321

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, Aug 30 2016

STATUS

approved

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Last modified February 22 19:34 EST 2018. Contains 299469 sequences. (Running on oeis4.)