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.

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

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Feb 09 2020

Keywords

Examples

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

Links

Crossrefs

Cf. A005238, A062327, A332312, A332314.

Programs

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

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 *)

A332388 Numbers k such that k, k + 1, k + 2 and k + 3 have the same number of divisors in Eisenstein integers.

Original entry on oeis.org

34193750, 76788050, 78267398, 113004199, 135383873, 148843670, 170293249, 199259222, 311313398, 318128599, 364828550, 368222599, 381026822, 384839047, 420686749, 428129222, 430154150, 432466824, 450050450, 462825847, 492828521, 510703975, 517126773, 518268772
Offset: 1

Views

Author

Amiram Eldar, Feb 10 2020

Keywords

Examples

			34193750 is a term since 34193750, 34193751, 34193752 and 34193750 each have 24 divisors in Eisenstein integers.

Crossrefs

Cf. A006601, A319442, A332314, A332386, A332387.

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]; m = 4; s = eisNumDiv /@ 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], {eisNumDiv[n]}]]; seq

A355712 Starts of runs of 4 consecutive numbers with the same number of 5-smooth divisors.

Original entry on oeis.org

28374, 133623, 136374, 187623, 190374, 298374, 349623, 352374, 457623, 460374, 511623, 619623, 622374, 673623, 676374, 781623, 838374, 943623, 946374, 997623, 1000374, 1108374, 1159623, 1162374, 1267623, 1270374, 1321623, 1429623, 1432374, 1483623, 1486374, 1591623
Offset: 1

Views

Author

Amiram Eldar, Jul 15 2022

Keywords

Comments

Numbers k such that A355583(k) = A355583(k+1) = A355583(k+2) = A355583(k+3).
Are there runs of 5 consecutive numbers with the same number of 5-smooth divisors? There are no such runs below 10^10.

Examples

			28374 is a term since A355583(28374) = A355583(28375) = A355583(28376) = A355583(28377) = 4.

Links

Crossrefs

Cf. A355583.
Subsequence of A355710 and A355711.
Similar sequences: A006601, A332314, A332388.

Programs

  • Mathematica
    f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 4; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^6}]; s
  • PARI
    s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); s2 = s(2); s3 = s(3); for(k = 4, 1.6e6, s4 = s(k); if(s1 == s2 && s2 == s3 && s3 == s4, print1(k-3,", ")); s1 = s2; s2 = s3; s3 = s4);
Showing 1-4 of 4 results.

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

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