A276319 Least number k such that phi(Sum_{j=0..n}{k-j}) = phi(Sum_{j=0..n}{k+j}).

1, 4, 9, 21, 10, 50, 27, 24, 36, 41, 25, 42, 54, 51, 147, 115, 34, 100, 61, 40, 133, 87, 55, 132, 121, 100, 102, 144, 46, 171, 167, 52, 89, 126, 82, 318, 122, 148, 121, 236, 85, 177, 144, 145, 216, 205, 115, 299, 216, 115, 206, 300, 94, 211, 246, 154, 192, 399

Offset

0,2

Links

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

Formula

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

Example

a(3) = 21 because phi(18+19+20+21) = phi(21+22+23+24) = 24.

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

Mathematica

Table[k = n; While[EulerPhi@ Sum[k - j, {j, 0, n}] != EulerPhi@ Sum[k + j, {j, 0, n}], k++]; k, {n, 0, 57}] (* Michael De Vlieger, Aug 30 2016 *)

Prog

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

Crossrefs

Cf. A000010, A276318, A276320.

Sequence in context: A225986 A147971 A197869 * A038805 A192162 A251545

Adjacent sequences: A276316 A276317 A276318 * A276320 A276321 A276322

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 30 2016

Status

approved