A332312 -id:A332312 - cp's OEIS frontend

A332313 Numbers k such that k, k + 1 and k + 2 have the same number of divisors in Gaussian integers.

23824, 38574, 52974, 62224, 71406, 105424, 110574, 191824, 201616, 209424, 240174, 249775, 282896, 285102, 297774, 326574, 340974, 375824, 393424, 407824, 440656, 451024, 496174, 509776, 553774, 587536, 599632, 600174, 606032, 623824, 628974, 631376, 667024, 672174

Offset: 1

Amiram Eldar, Feb 09 2020

nonn

			23824 is a term since 23824, 23825 and 23826 each have 36 divisors in Gaussian integers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005238, A062327, A332312, A332314.

Flatten[Position[Partition[DivisorSigma[0, Range[3*10^5], GaussianIntegers -> True], 3, 1], {x_, x_, x_}]] (* after Harvey P. Dale at A005238 *)

A332386 Numbers k such that k and k + 1 have the same number of divisors in Eisenstein integers.

Original entry on oeis.org

3, 7, 32, 50, 68, 174, 184, 200, 212, 219, 247, 291, 328, 343, 368, 376, 435, 472, 495, 543, 579, 608, 644, 679, 712, 716, 723, 788, 795, 849, 860, 871, 874, 904, 932, 939, 1011, 1015, 1058, 1074, 1076, 1159, 1184, 1220, 1227, 1336, 1359, 1384, 1436, 1495, 1515

Offset: 1

Amiram Eldar, Feb 10 2020

nonn

			3 is a term since 3 and 4 both have 3 divisors in Eisenstein integers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005237, A319442, A332312, A332387, A332388.

f[p_, e_] := Switch[Mod[p, 3], 0, 2*e + 1, 1, (e + 1)^2, 2, e + 1]; eisNumDiv[1] = 1; eisNumDiv[n_] := Times @@ f @@@ FactorInteger[n]; SequencePosition[eisNumDiv /@ Range[1520], {x_, x_}][[All, 1]] (* after Harvey P. Dale at A005237 *)

A332314 Numbers k such that k, k + 1, k + 2 and k + 3 have the same number of divisors in Gaussian integers.

Original entry on oeis.org

263449773, 334047725, 760228973, 862305773, 1965540624, 2136055725, 2362380525, 2477365422, 2515570575, 2613782223, 2939626925, 3181603023, 3814526223, 3987335022, 4610697039, 4771214574, 4981539822, 5018728272, 5035157775, 5186567824, 6189727725, 6329159823, 6569396973

Offset: 1

Amiram Eldar, Feb 09 2020

nonn

			263449773 is a term since 263449773, 263449774, 263449775 and 263449776 each have 72 divisors in Gaussian integers.

Cf. A006601, A062327, A332312, A332313.

gaussNumDiv[n_] := DivisorSigma[0, n, GaussianIntegers -> True]; m = 4; s = gaussNumDiv /@ Range[m]; seq = {}; n = m + 1; While[Length[seq] < 10, If[Length @ Union[s] == 1, AppendTo[seq, n - m + 1]]; n++; s = Join[Rest[s], {gaussNumDiv[n]}]]; seq

cp's OEIS Frontend

A332313 Numbers k such that k, k + 1 and k + 2 have the same number of divisors in Gaussian integers.

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A332386 Numbers k such that k and k + 1 have the same number of divisors in Eisenstein integers.

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Mathematica

A332314 Numbers k such that k, k + 1, k + 2 and k + 3 have the same number of divisors in Gaussian integers.

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Mathematica