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 1-3 of 3 results.

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

Views

Author

Amiram Eldar, Feb 10 2020

Keywords

Examples

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

Links

Crossrefs

Cf. A005237, A319442, A332312, A332387, 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]; SequencePosition[eisNumDiv /@ Range[1520], {x_, x_}][[All, 1]] (* after Harvey P. Dale at A005237 *)

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 *)

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 1-3 of 3 results.

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

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