cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A332312 Numbers k such that k and k + 1 have the same number of divisors in Gaussian integers.

Original entry on oeis.org

62, 153, 175, 206, 278, 404, 422, 494, 657, 774, 801, 833, 854, 873, 891, 926, 1017, 1070, 1126, 1142, 1233, 1322, 1424, 1502, 1617, 1718, 1737, 1881, 1910, 1953, 2097, 2222, 2302, 2673, 2694, 2793, 2798, 2817, 2825, 2961, 2996, 3014, 3174, 3177, 3266, 3446, 3577
Offset: 1

Views

Author

Amiram Eldar, Feb 09 2020

Keywords

Examples

			62 is a term since both 62 and 63 have 6 divisors in Gaussian integers.

Links

Crossrefs

Cf. A005237, A062327, A332313, A332314.

Programs

  • Mathematica
    SequencePosition[DivisorSigma[0, Range[3500], GaussianIntegers -> True], {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

Views

Author

Amiram Eldar, Feb 09 2020

Keywords

Examples

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

Crossrefs

Cf. A006601, A062327, A332312, A332313.

Programs

  • Mathematica
    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

A332387 Numbers k such that k, k + 1 and k + 2 have the same number of divisors in Eisenstein integers.

Original entry on oeis.org

13448, 27848, 75774, 135400, 243338, 276123, 396950, 452823, 497575, 524823, 565674, 587575, 632224, 639848, 719223, 769316, 861123, 935799, 1060904, 1073875, 1153023, 1204312, 1308856, 1366624, 1413498, 1490599, 1555975, 1565223, 1601798, 1767424, 1902774, 1923295
Offset: 1

Views

Author

Amiram Eldar, Feb 10 2020

Keywords

Examples

			13448 is a term since 13448, 13449 and 13450 each have 12 divisors in Eisenstein integers.

Links

Crossrefs

Cf. A005238, A319442, A332313, A332386, A332388.

Programs

  • Mathematica
    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]; Flatten[Position[Partition[ eisNumDiv /@ Range[10^6], 3, 1], {x_, x_, x_}]] (* after Harvey P. Dale at A005238 *)

A355711 Starts of runs of 3 consecutive numbers with the same number of 5-smooth divisors.

Original entry on oeis.org

33, 85, 93, 145, 213, 265, 393, 445, 453, 475, 505, 633, 685, 753, 805, 813, 865, 933, 985, 993, 1045, 1113, 1165, 1293, 1345, 1353, 1405, 1430, 1533, 1585, 1624, 1653, 1705, 1713, 1765, 1833, 1885, 1893, 1945, 2013, 2065, 2193, 2245, 2253, 2275, 2305, 2433, 2485
Offset: 1

Views

Author

Amiram Eldar, Jul 15 2022

Keywords

Comments

Numbers k such that A355583(k) = A355583(k+1) = A355583(k+2).

Examples

			33 is a term since A355583(33) = A355583(34) = A355583(35) = 2.

Links

Crossrefs

Cf. A355583.
Subsequence of A355710.
A355712 is a subsequence.
Similar sequences: A005238, A006073, A045939, A332313, A332387.

Programs

  • Mathematica
    f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 3; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 2500}]; s
  • PARI
    s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); s2 = s(2); for(k = 3, 2500, s3 = s(k); if(s1 == s2 && s2 == s3, print1(k-2,", ")); s1 = s2; s2 = s3);
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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