A348335 -id:A348335 - cp's OEIS frontend

A348688 a(n) = sigma(n) + sigma(n+1) + sigma(n+2) - sigma(n+3), where sigma is the sum of divisors.

1, 8, 5, 17, 11, 22, 18, 34, 15, 44, 30, 42, 31, 61, 34, 68, 35, 69, 58, 86, 32, 89, 73, 93, 57, 108, 54, 126, 71, 119, 89, 117, 59, 155, 117, 133, 64, 164, 92, 184, 98, 146, 134, 186, 74, 187, 136, 202, 124, 209, 104, 200, 126, 232, 182, 230, 62, 256, 194, 222, 135, 243, 171, 287, 170

Offset: 1

Michel Marcus, Oct 29 2021

sign

Michel Marcus, Table of n, a(n) for n = 1..11000

Cf. A000203, A348335, A348689, A348698 (a(n) <= 0).

Array[#+#2+#3-#4&@@DivisorSigma[1,{#,#+1,#+2,#+3}]&,100] (* Giorgos Kalogeropoulos, Oct 29 2021 *)

a(n) = sigma(n) + sigma(n+1) + sigma(n+2) - sigma(n+3);

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).

Original entry on oeis.org

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

Metin Sariyar, Nov 01 2021

nonn

			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.

David A. Corneth, Table of n, a(n) for n = 1..102
David A. Corneth, Upper bounds on some terms <= 10^13

Cf. A000005, A005237, A348335.

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 *)

a(n) = my(k=1); while (sum(i=k, k+n-1, numdiv(i)) != numdiv(k+n), k++); k; \\ Michel Marcus, Nov 01 2021

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

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

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

cp's OEIS Frontend

A348688 a(n) = sigma(n) + sigma(n+1) + sigma(n+2) - sigma(n+3), where sigma is the sum of divisors.

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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).

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