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.

A152774 Number of proper divisors of the Fibonacci number A000045(n).

Original entry on oeis.org

0, 0, 1, 1, 1, 3, 1, 3, 3, 3, 1, 14, 1, 3, 7, 7, 1, 15, 3, 15, 7, 3, 1, 71, 5, 3, 15, 15, 1, 63, 3, 15, 7, 3, 7, 159, 7, 7, 7, 63, 3, 63, 1, 31, 31, 7, 1, 335, 7, 47, 7, 15, 3, 127, 15, 95, 31, 7, 3, 959, 3, 7, 31, 63, 7, 63, 7, 31, 31, 127, 3, 1535, 3, 15, 47, 31, 15, 127, 3
Offset: 1

Views

Author

Omar E. Pol, Jan 17 2009

Keywords

Links

Crossrefs

Cf. A000005, A032741, A063375, A074283, A152990.

Programs

  • Mathematica
    a[n_] := DivisorSigma[0, Fibonacci[n]] - 1; Array[a, 100] (* Amiram Eldar, Apr 07 2024 *)
  • PARI
    a(n) = numdiv(fibonacci(n)) - 1; \\ Amiram Eldar, Apr 07 2024

Formula

a(n) = A000005(A000045(n))-1 = A032741(A000045(n)) = A063375(n)-1.

A162196 Sum of proper divisors minus the number of proper divisors of nonprime number A018252(n).

Original entry on oeis.org

0, 1, 3, 4, 2, 5, 11, 7, 6, 11, 16, 17, 8, 11, 29, 4, 13, 10, 23, 35, 26, 12, 17, 10, 47, 19, 14, 43, 47, 35, 28, 23, 67, 6, 38, 18, 41, 59, 14, 57, 20, 29, 97, 31, 36, 57, 16, 71, 53, 24, 67, 112, 37, 44, 59, 16, 83, 97, 36, 41, 129, 20, 43, 30
Offset: 1

Views

Author

Omar E. Pol, Jul 04 2009

Keywords

Comments

Also, zero together with the positive integers of A152770.
Note that the k-th positive integer of this sequence is equal to the sum of proper divisors minus the number of proper divisors of the composite number A002808(k).

Crossrefs

Cf. A001065, A018252, A002808, A032741, A152770, A152988, A152989, A152990, A162194, A162195.

Programs

Formula

a(n) = A152770(A018252(n)).
a(n) = A001065(A018252(n)) - A032741(A018252(n)).

A154349 Sum of proper divisors minus the number of proper divisors of Motzkin number A001006(n).

Original entry on oeis.org

0, 0, 0, 1, 2, 8, 18, 0, 34, 170, 1643, 3603, 0, 25118, 139063, 474559, 284490, 984006, 6536387, 24265729, 18678366, 96214018, 277799290, 1282283434, 2077807072, 1899874612, 19252363859, 44221482383, 1967547352, 29743945396, 1265868622
Offset: 0

Views

Author

Omar E. Pol, Jan 07 2009

Keywords

Comments

Note that, if a(n) != 0 then Motzkin number A001006(n) is a composite number (A002808), otherwise A001006(n) is a noncomposite number (A008578). See A152770.

Links

Crossrefs

Cf. A001006, A001065, A002808, A032741, A008578, A152770, A152981, A152982, A152983, A152988, A152990.

Programs

  • Maple
    with(numtheory): M := proc (n) options operator, arrow: (sum((-1)^j*binomial(n+1, j)*binomial(2*n-3*j, n), j = 0 .. floor((1/3)*n)))/(n+1) end proc: seq(sigma(M(n))-M(n)-tau(M(n))+1, n = 0 .. 30); # Emeric Deutsch, Jan 12 2009
  • Mathematica
    mot[0] = 1; mot[n_] := mot[n] = mot[n - 1] + Sum[mot[k] * mot[n - 2 - k], {k, 0, n - 2}]; diff[n_] := DivisorSigma[1, n] - DivisorSigma[0, n] - n + 1; Table[diff[mot[n]], {n, 0, 30}] (* Amiram Eldar, Nov 26 2019 *)

Formula

a(n) = A001065(A001006(n)) - A032741(A001006(n)) = A152770(A001006(n)).

Extensions

Extended by Emeric Deutsch, Jan 12 2009
Showing 1-3 of 3 results.

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

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