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.

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 *)

A355710 Numbers k such that k and k+1 have the same number of 5-smooth divisors.

Original entry on oeis.org

2, 21, 33, 34, 38, 57, 85, 86, 93, 94, 104, 116, 122, 141, 145, 146, 154, 158, 171, 177, 182, 189, 201, 205, 213, 214, 218, 237, 265, 266, 273, 296, 302, 321, 326, 332, 334, 338, 344, 357, 362, 381, 385, 387, 393, 394, 398, 417, 445, 446, 453, 454, 475, 476, 482
Offset: 1

Views

Author

Amiram Eldar, Jul 15 2022

Keywords

Comments

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

Examples

			2 is a term since A355583(2) = A355583(3) = 2.

Links

Crossrefs

Cf. A355583, A355709 (3-smooth analog).
Subsequences: A355711, A355712.
Similar sequences: A005237, A006049, A332386, A343819, A344312, A344313, A344314, A348345.

Programs

  • Mathematica
    s[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); Select[Range[500], s[#] == s[#+1] &]
  • PARI
    s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); for(k = 2, 500, s2 = s(k); if(s1 == s2, print1(k-1,", ")); s1 = s2);

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

A355709 Numbers k such that k and k+1 have the same number of 3-smooth divisors.

Original entry on oeis.org

2, 14, 21, 33, 38, 44, 50, 57, 69, 74, 80, 86, 93, 99, 105, 110, 116, 122, 129, 135, 141, 146, 158, 165, 171, 177, 182, 194, 201, 213, 218, 230, 237, 249, 254, 260, 266, 273, 285, 290, 296, 302, 309, 315, 321, 326, 332, 338, 345, 357, 362, 374, 381, 387, 393, 398
Offset: 1

Views

Author

Amiram Eldar, Jul 15 2022

Keywords

Comments

Numbers k such that A072078(k) = A072078(k+1).
This sequence is infinite since it includes all the numbers of the form 3*(2^(2*k+1)-1), with k>=1.

Examples

			2 is a term since A072078(2) = A072078(3) = 2.

Links

Crossrefs

Cf. A072078, A355710 (5-smooth analog).
Similar sequences: A005237, A006049, A332386, A343819, A344312, A344313, A344314, A348345.

Programs

  • Mathematica
    s[n_] := Times @@ (1 + IntegerExponent[n, {2, 3}]); Select[Range[400], s[#] == s[#+1] &]
  • PARI
    s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1);
s1 = s(1); for(k = 2, 400, s2 = s(k); if(s1 == s2, print1(k-1,", ")); s1 = s2);
Showing 1-4 of 4 results.

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

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