A276320 Least number k such that d(Sum_{j=0..n}{k-j}) = d(Sum_{j=0..n}{k+j}).

1, 2, 5, 4, 5, 6, 8, 12, 9, 10, 12, 15, 13, 15, 15, 16, 17, 18, 20, 21, 21, 24, 30, 30, 25, 26, 29, 28, 33, 30, 32, 32, 36, 35, 35, 36, 39, 44, 42, 45, 42, 45, 45, 48, 45, 46, 47, 60, 50, 51, 53, 54, 57, 54, 56, 63, 63, 58, 59, 60, 62, 63, 72, 65, 69, 66, 70, 68

Offset

0,2

Links

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

Formula

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

Example

a(8) = 12 because d(5+6+7+8+9+10+11+12) = d(12+13+14+15+16+17+18+19) = 6.

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 tau((n+1)*(2*k-n)/2)=tau((n+1)*(2*k+n)/2)
then print(k); break; fi; od; od; end: P(10^9);

Mathematica

Table[k = n; While[DivisorSigma[0, Sum[k - j, {j, 0, n}]] != DivisorSigma[0, Sum[k + j, {j, 0, n}]], k++]; k, {n, 0, 67}] (* Michael De Vlieger, Aug 30 2016 *)

Prog

(PARI) a(n) = {if (n==0, k = 1, k = n); while (numdiv((n+1)*(2*k-n)/2) != numdiv((n+1)*(2*k+n)/2), k++); k; } \\ Michel Marcus, Aug 31 2016

Crossrefs

Cf. A000005, A276318, A276319.

Sequence in context: A102066 A279404 A072970 * A011036 A086267 A348027

Adjacent sequences: A276317 A276318 A276319 * A276321 A276322 A276323

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 30 2016

Status

approved