A350935 -id:A350935 - cp's OEIS frontend

A350934 a(n) is the smallest number m such that tau(m - 1) = tau(m + 1) = tau(m) + n or 0 if no such m exists, where tau(k) = A000005(k).

34, 9, 7, 964324, 19, 3822025, 41, 15129, 341, 427166224, 199, 700569, 1241, 11923111249, 919, 12376324, 6641, 34539129, 12221, 363016809, 3401, 56776225, 5741, 199809, 52865, 48045571249, 47081, 3764067904, 21113, 19035769, 18089, 145371249, 59291, 2219069449

Offset: 0

Jaroslav Krizek, Jan 25 2022

nonn

Corresponding values of tau(a(n)): 4, 3, 2, 9, 2, 27, 2, 9, 4, 15, 2, 21, 4, 27, 2, 9, 4, 15, 6, 45, 4, 27, 2, 9, 8, 15, 6, 21, 4, 3, 2, 9, 4, 15, ...
Triples of [tau(a(n) - 1), tau(a(n)), tau(a(n) + 1)] = [tau(a(n)) + n, tau(a(n)), tau(a(n)) + n]: [4, 4, 4], [4, 3, 4], [4, 2, 4], [12, 9, 12], [6, 2, 6], [32, 27, 32], [8, 2, 8], [16, 9, 16], [12, 4, 12], ...
If n is odd then a(n) is a square. - Amiram Eldar, Jan 26 2022

			a(3) = 964324 because 964324 is the smallest number m such that tau(m-1) = tau(m+1) = tau(m)+3; tau(964323) = tau(964325) = tau(964324)+3 = 9+3 = 12.

Cf. A000005, A190646, A350132, A350935, A350936.

Magma
```
Ax:=func; [Ax(n): n in [0..8]]
```

seq[m_, nmax_] := Module[{s = Table[0, {m + 1}], c = 0, d1 = 1, d2 = 2, n = 3, d, k}, While[c < m + 1 && n < nmax, d = DivisorSigma[0, n]; If[d1 == d, k = d - d2 + 1; If[k >= 1 && k <= m + 1 && s[[k]] == 0, s[[k]] = n - 1; c++]]; n++; d1 = d2; d2 = d]; TakeWhile[s, # > 0 &]]; seq[8, 10^7] (* Amiram Eldar, Jan 26 2022 *)

More terms from Amiram Eldar, Jan 26 2022

A350936 a(n) is the smallest number m such that tau(m) = ntau(m-1) = ntau(m+1) or 0 if no such m exists, where tau(k) = A000005(k).

Original entry on oeis.org

34, 6, 12, 30, 816, 60, 192, 270, 180, 240, 56320, 420, 233472, 2112, 1620, 1320, 2162688, 2340, 786432, 3120, 4800, 15360, 62914560, 3360, 172368, 724992, 6300, 29760, 24964497408, 12240, 35433480192, 7560, 599040, 15138816, 81648, 21600, 7215545057280

Offset: 1

Jaroslav Krizek, Jan 25 2022

nonn

Corresponding values of tau(a(n)): 4, 4, 6, 8, 20, 12, 14, 16, 18, 20, 44, 24, 52, 28, 30, 32, 68, 36, 38, 40, 42, 44, 92, 48, 100, 52, 54, 56, 116, 60, 124, 64, 132, 136, 70, 72, 296, ...

Triples of [tau(a(n) - 1), tau(a(n)), tau(a(n) + 1)] = [tau(a(n)) / n, tau(a(n)), tau(a(n)) / n]: [4, 4, 4], [2, 4, 2], [2, 6, 2], [2, 8, 2], [4, 20, 4], [2, 12, 2], [2, 14, 2], [2, 16, 2], [2, 18, 2], [2, 20, 2], [4, 44, 4], ...

			a(3) = 12 because 12 is the smallest number m such that tau(m) = 3 * tau(m-1) = 3 * tau(m+1); tau(12) = 3 * tau(11) = 3 * tau(13) = 3 * 2 = 6.

Cf. A000005, A190646, A350132, A350934, A350935.

Magma
```
Ax:=func; [Ax(n): n in [1..16]]
```

a(23)-a(37) from Jon E. Schoenfield, Jan 25 2022

cp's OEIS Frontend

A350934 a(n) is the smallest number m such that tau(m - 1) = tau(m + 1) = tau(m) + n or 0 if no such m exists, where tau(k) = A000005(k).

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A350936 a(n) is the smallest number m such that tau(m) = ntau(m-1) = ntau(m+1) or 0 if no such m exists, where tau(k) = A000005(k).

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cp's OEIS Frontend

A350934 a(n) is the smallest number m such that tau(m - 1) = tau(m + 1) = tau(m) + n or 0 if no such m exists, where tau(k) = A000005(k).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

Extensions

A350936 a(n) is the smallest number m such that tau(m) = n*tau(m-1) = n*tau(m+1) or 0 if no such m exists, where tau(k) = A000005(k).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Extensions

A350936 a(n) is the smallest number m such that tau(m) = ntau(m-1) = ntau(m+1) or 0 if no such m exists, where tau(k) = A000005(k).