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 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, 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 (list; graph; refs; listen; history; text; internal format)
 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 A040348 Adjacent sequences:  A274246 A274247 A274248 * A274250 A274251 A274252 KEYWORD nonn,easy AUTHOR Paolo P. Lava, Jun 16 2016 STATUS approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)