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 1-5 of 5 results.

A324825 Number of divisors d of n such that A323243(d) is odd; number of terms of A324813 larger than 1 that divide n.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 2, 2, 1, 2, 2, 3, 1, 4, 1, 2, 2, 2, 1, 2, 1, 4, 2, 2, 1, 2, 3, 2, 2, 2, 1, 4, 1, 2, 3, 1, 2, 3, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 1, 2, 1, 4, 2, 2, 2, 2, 1, 4, 3, 2, 2, 2, 2, 2, 1, 3, 2, 4, 1, 3, 1, 2, 4
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2019

Keywords

Comments

Inverse Möbius transform of A324823.

Crossrefs

Programs

  • PARI
    A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552 by David A. Corneth
    A324823(n) = if(1==n,0, n=A156552(n); (issquare(n) || (!(n%2) && issquare(n/2))));
    A324825(n) = sumdiv(n,d,A324823(d));
    
  • PARI
    A324825(n) = sumdiv(n,d,A323243(d)%2); \\ This needs code also from A323243.

Formula

a(n) = Sum_{d|n} A324823(d).
a(p^k) = 1, for all primes p and exponents k >= 1.

A324830 Number of divisors d of n such that A323243(d) is a multiple of 3.

Original entry on oeis.org

1, 1, 2, 1, 1, 3, 2, 1, 3, 1, 1, 4, 2, 3, 3, 2, 1, 4, 2, 1, 4, 2, 1, 5, 1, 3, 4, 4, 2, 4, 1, 2, 3, 1, 3, 5, 2, 3, 4, 1, 1, 6, 2, 2, 5, 1, 1, 7, 3, 1, 3, 4, 2, 6, 1, 5, 4, 3, 1, 5, 2, 2, 6, 2, 3, 6, 1, 1, 3, 5, 2, 7, 1, 3, 4, 4, 3, 6, 2, 2, 5, 1, 1, 8, 2, 3, 4, 3, 2, 7, 4, 1, 3, 2, 3, 8, 1, 5, 5, 2, 2, 5, 1, 5, 7
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2019

Keywords

Crossrefs

Programs

Formula

a(n) = A000005(n) - (A324831(n) + A324832(n)).
For all n >= 1, a(A000040(n)) = 2-A000035(n).

A324831 Number of divisors d of n such that A323243(d) == 1 (mod 3).

Original entry on oeis.org

0, 1, 0, 2, 1, 1, 0, 2, 0, 3, 1, 2, 0, 1, 1, 2, 1, 1, 0, 4, 0, 2, 1, 2, 2, 1, 0, 2, 0, 3, 1, 2, 1, 2, 1, 3, 0, 1, 0, 4, 1, 1, 0, 3, 1, 2, 1, 2, 0, 5, 1, 2, 0, 1, 3, 2, 0, 1, 1, 4, 0, 2, 0, 2, 1, 2, 1, 4, 1, 3, 0, 3, 1, 1, 2, 2, 1, 2, 0, 4, 0, 2, 1, 3, 2, 1, 0, 3, 0, 3, 0, 4, 1, 2, 1, 2, 1, 1, 1, 6, 0, 2, 1, 2, 1
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2019

Keywords

Crossrefs

Programs

Formula

a(n) = A000005(n) - (A324830(n) + A324832(n)).
For all n >= 1, a(A000040(n)) = A000035(n).

A324826 Number of divisors d of n such that A323243(d) is either 0 or 1 (mod 4).

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 4, 2, 3, 1, 4, 1, 2, 1, 5, 1, 3, 1, 5, 1, 3, 1, 6, 2, 3, 3, 4, 1, 4, 1, 6, 1, 3, 1, 6, 1, 2, 2, 7, 1, 2, 1, 5, 3, 3, 1, 8, 2, 4, 2, 5, 1, 4, 1, 6, 2, 2, 1, 8, 1, 3, 3, 7, 1, 4, 1, 5, 1, 3, 1, 9, 1, 3, 2, 4, 1, 5, 1, 9, 4, 3, 1, 6, 2, 3, 2, 7, 1, 6, 1, 5, 1, 3, 2, 10, 1, 4, 3, 7, 1, 4, 1, 7, 2
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2019

Keywords

Crossrefs

Programs

Formula

a(n) = A000005(n) - A324827(n).
a(p) = 1 for all odd primes p.

A324827 Number of divisors d of n such that A323243(d) is either 2 or 3 (mod 4).

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 2, 3, 0, 1, 3, 1, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 0, 3, 1, 3, 3, 1, 2, 2, 1, 1, 6, 1, 1, 3, 1, 1, 2, 1, 2, 2, 1, 1, 4, 3, 2, 2, 2, 1, 4, 1, 1, 3, 0, 3, 4, 1, 1, 3, 5, 1, 3, 1, 1, 4, 2, 3, 3, 1, 1, 1, 1, 1, 6, 2, 1, 2, 1, 1, 6, 3, 1, 3, 1, 2, 2, 1, 2, 3, 2, 1, 4, 1, 1, 6
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2019

Keywords

Crossrefs

Programs

Formula

a(n) = A000005(n) - A324826(n).
a(p) = 1 for all odd primes p.
Showing 1-5 of 5 results.