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 1-2 of 2 results.

A263097 First differences of A263096.

Original entry on oeis.org

0, 1, 0, 1, 1, 2, 0, 1, 3, 3, 2, 3, 8, 2, 7, 5, 10, 20, 16, 14, 22, 19, 17, 8, 46, 12, 11, 53, 44, 75, 63, 56, 50, 130, 38, 71, 33, 191, 161, 270, 227, 201, 181, 467, 138, 256, 347, 509, 362, 491, 1045, 368, 513, 1251, 747, 1927, 568, 1057, 1431, 2097, 1494, 2025, 4308, 2946, 687, 6093, 4167, 8399, 1189, 1287, 4605, 6239, 9141, 6513, 8822, 18782, 15834, 26561, 22392, 37564, 16401, 32375, 17317, 12602
Offset: 1

Views

Author

Antti Karttunen, Oct 10 2015

Keywords

Comments

a(n) = number of perfect squares in range [A002182(n)+1 .. A002182(n+1)].

Examples

			A002182 begins as 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...
In range [2,2] there are no squares, so a(1) = 0.
In range [3,4] there is one square, so a(2) = 1.
In range [5,6] there are no squares, so a(3) = 0.
In range [7,12] there is one square, so a(4) = 1.
In range [13,24] there is one square, so a(5) = 1.
In range [25,36] there are two squares, so a(6) = 2.
In range [37,48] there are no squares, so a(7) = 0.
In range [49,60] there is one square, so a(8) = 1.
In range [61,120] there are three squares (64, 81, 100), thus a(9) = 3.
		

Crossrefs

Programs

Formula

a(n) = A263096(n+1) - A263096(n).

A263098 a(n) = Max( tau(k) : k=1,2,3,...,n^2 ) where tau(k) = A000005(k) is the number of divisors of k.

Original entry on oeis.org

1, 3, 4, 6, 8, 9, 10, 12, 12, 12, 16, 16, 16, 18, 18, 20, 20, 20, 24, 24, 24, 24, 24, 24, 24, 24, 30, 30, 32, 32, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 72
Offset: 1

Views

Author

Antti Karttunen, Oct 10 2015

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Max[DivisorSigma[0, #] & /@ Range[n^2]], {n, 101}] (* Michael De Vlieger, Oct 11 2015 *)
  • PARI
    A070319(n, m=1, s=2)={for(k=s, n, mM. F. Hasler, Sep 12 2012
    A263098 = n -> A070319(n^2); \\ Slow without memoization.
    for(n=1, 2080, write("b263098.txt", n, " ", A263098(n)));
    
  • Scheme
    (define (A263098 n) (A070319 (A000290 n)))

Formula

a(n) = A070319(A000290(n)).
Showing 1-2 of 2 results.