A274249 a(n) is the least number m such that Sum_{k=0..(n-1)}{d(m + k)} | Sum_{k=0..(n-1)}{m+k}, where d(x) is the number of divisors of x.

1, 1, 19, 4, 4, 8, 65, 2, 36, 6, 30, 5, 39, 27, 13, 105, 8, 114, 11, 22, 68, 191, 130, 51, 38, 70, 31, 117, 163, 69, 286, 313, 86, 159, 15, 145, 90, 574, 244, 45, 100, 62, 105, 457, 61, 9, 1, 139, 7, 7, 60, 231, 347, 144, 344, 3, 36, 489, 103, 185, 292, 682, 19

Offset

1,3

Links

Paolo P. Lava, Table of n, a(n) for n = 1..2000

Formula

a( A160922(n)) = 1. - Michel Marcus, Jun 22 2016

Example

a(3) = 19 because it is the least number such that (19 + 20 + 21) / (d(19) + d(20) + d(21)) = 60 / (2 + 6 + 4) = 60 / 12 = 5 is integer.

Maple

with(numtheory): P:=proc(q) local i, k, n;
for i from 1 to q do for n from 1 to q do
if type(i*(2*n+i-1)/(2*add(tau(n+k), k=0..i-1)), integer)
then print(n); break; fi; od; od; end: P(10^6);

Mathematica

Table[m = 1; While[! Divisible[Sum[m + k, {k, 0, n - 1}], Sum[ DivisorSigma[0, m + k], {k, 0, n - 1}]], m++]; m, {n, 63}] (* Michael De Vlieger, Jun 22 2016 *)

Prog

(PARI) a(n) = {my(m = 1); while (sum(k=0, n-1, m+k) % sum(k=0, n-1, numdiv(m+k)), m++); m; } \\ Michel Marcus, Jun 20 2016

Crossrefs

Cf. A000005, A160922.

Sequence in context: A317319 A002206 A040349 * A040350 A089572 A358929

Adjacent sequences: A274246 A274247 A274248 * A274250 A274251 A274252

Keyword

nonn,easy

Author

Paolo P. Lava, Jun 16 2016

Status

approved