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.

A356063 a(n) is the new Lucas divisor that appears at the step A356062(n).

Original entry on oeis.org

1, 2, 4, 3, 18, 7, 11, 76, 322, 29, 1364, 123, 47, 199, 24476, 843, 5778, 521
Offset: 1

Views

Author

Bernard Schott, Jul 25 2022

Keywords

Comments

The sequence is not monotonic.
Conjecture: the sequence is well defined, i.e., it is not possible that two new Lucas divisors arrive while one disappears for some step in A356062.

Examples

			a(1) = 1 because the smallest integer that has only one Lucas divisor is 1 since 1 is the smallest Lucas number in A000032.
A356062(6) = 252 and the set of the six Lucas divisors of 252 is {1, 2, 3, 4, 7, 18}. Then, A356062(7) = 2772 and the set of the seven Lucas divisors of 2772 is {1, 2, 3, 4, 7, 11, 18}. The new Lucas divisor that appears in this set is 11, hence a(7) = 11.

Crossrefs

Cf. A000032, A304092, A349100, A356062.

A356123 Least Lucas number with n Lucas divisors.

Original entry on oeis.org

1, 2, 4, 18, 1364, 1860498, 2537720636, 6440026026380244498, 8784200221406821330636, 77162173529763648886126034136172445632164498, 4365101043708483494615466932242949707161871659736799144058331102381689400753867700636
Offset: 1

Views

Author

Michel Marcus, Jul 27 2022

Keywords

Links

Crossrefs

Cf. A000032, A102460, A304092, A356062, A356122, A356666.
Cf. A076985 (similar for Fibonacci numbers).

Programs

  • PARI
    L(n)=fibonacci(n+1)+fibonacci(n-1); \\ A000032
isld(n) = { my(u1=1, u2=3, old_u1); if(n<=2, sign(n), while(n>u2, old_u1=u1; u1=u2; u2=old_u1+u2); (u2==n)); }; \\ A102460
nbld(n) = sumdiv(n, d, isld(d)); \\ A304092
a(n) = my(k=0); while(nbld(L(k)) != n, k++); L(k);
  • PARI
    countLd(n) = my(c=0,x=2,y=1); while(x <= n, if(n%x == 0, c++); [x,y]=[y,x+y]); c;
a(n) = if(n==1, return(1)); my(x=2,y=1); while(1, if(countLd(x) == n, return(x)); [x,y]=[y,x+y]); \\ Daniel Suteu, Aug 24 2022

Formula

a(n) = A000032(A356666(n)). - Daniel Suteu, Aug 24 2022

Extensions

a(11) from Daniel Suteu, Aug 06 2022

A356122 Number of Lucas divisors of the n-th Lucas number.

Original entry on oeis.org

2, 1, 2, 3, 2, 2, 4, 2, 2, 4, 3, 2, 4, 2, 3, 5, 2, 2, 5, 2, 3, 5, 3, 2, 4, 3, 3, 5, 3, 2, 6, 2, 2, 5, 3, 4, 5, 2, 3, 5, 3, 2, 6, 2, 3, 7, 3, 2, 4, 3, 4, 5, 3, 2, 6, 4, 3, 5, 3, 2, 6, 2, 3, 7, 2, 4, 6, 2, 3, 5, 5, 2, 5, 2, 3, 7, 3, 4, 6, 2, 3, 6, 3, 2, 6, 4, 3, 5, 3, 2, 8, 4, 3, 5, 3, 4, 4, 2, 4, 7
Offset: 0

Views

Author

Michel Marcus, Jul 27 2022

Keywords

Links

Crossrefs

Cf. A000032, A102460, A304092, A356062, A356123.
Cf. A076984 (similar for Fibonacci numbers).

Programs

  • PARI
    L(n)=fibonacci(n+1)+fibonacci(n-1); \\ A000032
isld(n) = { my(u1=1, u2=3, old_u1); if(n<=2, sign(n), while(n>u2, old_u1=u1; u1=u2; u2=old_u1+u2); (u2==n)); }; \\ A102460
nbld(n) = sumdiv(n, d, isld(d)); \\ A304092
a(n) = nbld(L(n));
  • PARI
    a(n) = if(n==1, return(1)); my(k=fibonacci(n+1)+fibonacci(n-1),c=0,x=2,y=1); while(x <= k, if(k%x == 0, c++); [x,y]=[y,x+y]); c; \\ Daniel Suteu, Aug 25 2022

Formula

a(n) = A304092(A000032(n)).
Showing 1-3 of 3 results.

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