A348837 a(n) is the smallest k such that the sum of the number of divisors of the n numbers from k to k+n-1 equals tau(k+n).

2, 10, 93, 236, 355, 2634, 2873, 5032, 11331, 20150, 18889, 80628, 55427, 207886, 205905, 371264, 369583, 617742, 166301, 1436380, 720699, 2227658, 1081057, 831576, 4633175, 3326374, 2633373, 5045012, 11850271, 6683010, 11642369, 9979168, 9424767, 8648606, 24418765

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..102

David A. Corneth, Upper bounds on some terms <= 10^13

Example

a(1) = 2 because tau(2) = tau(3) = 2; a(1) = A005237(1).
a(2) = 10 because tau(10) + tau(11) = 4 + 2 =  6, the same as tau(12) = 6.
a(3) = 93 because tau(93) + tau(94) + tau(95) = 4 + 4 + 4 = 12, the same as tau(96) = 12.

Mathematica

a[n_] := Module[{div = DivisorSigma[0, Range[n]], k = n + 1}, While[(d = DivisorSigma[0, k]) != Plus @@ div, div = Join[Drop[div, 1], {d}]; k++]; k - n]; Array[a, 20] (* Amiram Eldar, Nov 01 2021 *)

Prog

(PARI) a(n) = my(k=1); while (sum(i=k, k+n-1, numdiv(i)) != numdiv(k+n), k++); k; \\ Michel Marcus, Nov 01 2021
(PARI) a(n)=my(v=vector(n, k, numdiv(k)), s=vecsum(v), t, i=n); forfactored(k=n+1, 2^63-1, t=numdiv(k); if(s==t, return(k[1]-n)); if(i++>n, i=1); s+=t-v[i]; v[i]=t) \\ Charles R Greathouse IV, Nov 01 2021

Crossrefs

Cf. A000005, A005237, A348335.

Sequence in context: A063385 A293709 A063393 * A349880 A260339 A205320

Adjacent sequences: A348834 A348835 A348836 * A348838 A348839 A348840

Keyword

nonn

Author

Metin Sariyar, Nov 01 2021

Extensions

a(21)-a(26) from Michel Marcus, Nov 01 2021

a(27)-a(35) from Amiram Eldar, Nov 01 2021

Status

approved