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.

A324594 a(n) is the smallest number k such that n consecutive integers starting at k have the same number of nonprime divisors (A033273).

Original entry on oeis.org

1, 1, 1, 19940, 204323, 294590, 310042685, 2587701932494, 2587701932494
Offset: 1

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Author

Ilya Gutkovskiy, Sep 03 2019

Keywords

Examples

			19940 has 9 nonprime divisors {1, 4, 10, 20, 1994, 3988, 4985, 9970, 19940}, 19941 has 9 nonprime divisors {1, 51, 69, 289, 391, 867, 1173, 6647, 19941}, 19942 has 9 nonprime divisors {1, 26, 118, 169, 338, 767, 1534, 9971, 19942} and 19943 has 9 nonprime divisors {1, 49, 77, 259, 407, 539, 1813, 2849, 19943}. These the first 4 consecutive numbers with the same number of nonprime divisors, so a(4) = 19940.
		

Crossrefs

Programs

  • C
    See Links section.

Extensions

a(7) from Rémy Sigrist, Sep 04 2019
a(8)-a(9) from Giovanni Resta, Sep 04 2019

A338628 a(n) is the smallest number k such that n consecutive integers starting at k have the same number of square divisors (A046951).

Original entry on oeis.org

1, 1, 1, 844, 3624, 22020, 671346, 8870024, 264459172, 463239475, 1407472722, 108494875170, 12385053656370, 145065154350545
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 04 2020

Keywords

Examples

			844 has 2 square divisors {1, 4}, 845 has 2 square divisors {1, 169}, 846 has 2 square divisors {1, 9} and 847 has 2 square divisors {1, 121}. These are the first 4 consecutive numbers with the same number of square divisors, so a(4) = 844.
		

Crossrefs

Programs

  • Mathematica
    Do[find = 0; k = 0; While[find == 0, k++; If[Length[Union[Table[Length[Select[Divisors[j], IntegerQ[Sqrt[#]] &]], {j, k, k + n - 1}]]] == 1, find = 1; Print[k]]], {n, 1, 7}]
  • PARI
    isok(n, k) = #Set(apply(x->sumdiv(x, d, issquare(d)), vector(n, i, k+i-1))) == 1;
    a(n) = my(k=1); while(! isok(n, k), k++); k; \\ Michel Marcus, Nov 05 2020

Extensions

a(8)-a(11) from Amiram Eldar, Nov 04 2020
a(12)-a(14) from Martin Ehrenstein, Jul 19 2023

A358044 a(n) is the smallest number k such that n consecutive integers starting at k have the same number of triangular divisors (A007862).

Original entry on oeis.org

1, 1, 55, 5402, 2515069
Offset: 1

Views

Author

Ilya Gutkovskiy, Oct 26 2022

Keywords

Comments

Any subsequent terms are > 10^10. - Lucas A. Brown, Jan 06 2023

Examples

			55 has 2 triangular divisors {1, 55}, 56 has 2 triangular divisors {1, 28} and 57 has 2 triangular divisors {1, 3}. These are the first 3 consecutive numbers with the same number of triangular divisors, so a(3) = 55.
		

Crossrefs

Showing 1-3 of 3 results.