A074788 -id:A074788 - cp's OEIS frontend

A294879 Number of proper divisors of n that are in Perrin sequence, A001608.

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 3, 2, 1, 0, 3, 1, 1, 1, 2, 0, 4, 0, 1, 1, 2, 2, 3, 0, 1, 1, 3, 0, 3, 0, 2, 2, 1, 0, 3, 1, 3, 2, 1, 0, 2, 1, 2, 1, 2, 0, 5, 0, 1, 2, 1, 1, 3, 0, 2, 1, 4, 0, 3, 0, 1, 2, 1, 1, 3, 0, 3, 1, 1, 0, 4, 2, 1, 2, 2, 0, 4, 1, 1, 1, 1, 1, 3, 0, 2, 1, 3, 0, 4, 0, 1, 3, 1, 0, 3, 0, 4, 1, 2, 0, 2, 1, 2, 2, 1, 2, 5, 0

Offset: 1

Antti Karttunen, Nov 10 2017

nonn

			For n = 22, with proper divisors [1, 2, 11], only 2 is in A001608, thus a(22) = 1.
For n = 121, with proper divisors [1, 11], neither of them is in A001608, thus a(121) = 0. Note that this is the first zero not in A008578.
For n = 644, with proper divisors [1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644], both 2 and 7 are in A001608, thus a(644) = 2.

Antti Karttunen, Table of n, a(n) for n = 1..24914

Cf. A001608, A014981, A074788, A294878, A294880.

Cf. also A293433, A293435.

A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]);
A294878(n) = { my(k=1,v); while((v=A001608(k))A294879(n) = sumdiv(n,d,(dA294878(d));

a(n) = Sum_{d|n, dA294878(d).

a(n) = A294880(n) - A294878(n).

A294880 Number of divisors of n that are in Perrin sequence, A001608.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 1, 1, 3, 0, 3, 0, 2, 2, 1, 1, 2, 0, 3, 2, 2, 0, 3, 1, 1, 1, 2, 1, 4, 0, 1, 1, 2, 2, 3, 0, 1, 2, 3, 0, 3, 0, 2, 2, 1, 0, 3, 1, 3, 3, 1, 0, 2, 1, 2, 1, 2, 0, 5, 0, 1, 2, 1, 1, 3, 0, 3, 1, 4, 0, 3, 0, 1, 2, 1, 1, 3, 0, 3, 1, 1, 0, 4, 2, 1, 2, 2, 0, 5, 1, 1, 1, 1, 1, 3, 0, 2, 1, 3, 0, 4, 0, 1, 3

Offset: 1

Antti Karttunen, Nov 10 2017

nonn

			For n = 22, with divisors [1, 2, 11, 22], both 2 and 22 are in A001608, thus a(22) = 2.
For n = 644, with divisors [1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644], 2, 7 and 644 are in A001608, thus a(644) = 3.

Antti Karttunen, Table of n, a(n) for n = 1..24914

Cf. A001608, A014981, A074788, A294878, A294879.

Cf. also A005086, A293431.

With[{s = LinearRecurrence[{0, 1, 1}, {3, 2, 5}, 15]}, Table[DivisorSum[n, 1 &, MemberQ[s, #] &], {n, 1, s[[-1]]}]] (* Amiram Eldar, Jan 01 2024 *)

A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]);
A294878(n) = { my(k=1,v); while((v=A001608(k))A294880(n) = sumdiv(n,d,A294878(d));

a(n) = Sum_{d|n} A294878(d).
a(n) = A294879(n) + A294878(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = -1/5 + Sum_{n>=3} 1/A001608(n) = 1.603595519775230150708... . - Amiram Eldar, Jan 01 2024

A112881 Indices of prime Perrin numbers; values of n such that A001608(n) is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 10, 12, 20, 21, 24, 34, 38, 75, 122, 166, 236, 355, 356, 930, 1042, 1214, 1461, 1622, 4430, 5802, 9092, 16260, 18926, 23698, 40059, 45003, 73807, 91405, 263226, 316872, 321874, 324098, 581132, 939189, 1034005, 1430138

Offset: 1

Eric W. Weisstein, Oct 05 2005

Eric Weisstein's World of Mathematics, Perrin Sequence
Eric Weisstein's World of Mathematics, Integer Sequence Primes

Cf. A001608, A074788.

a(34) from Eric W. Weisstein, Oct 06 2005
a(35) = 263226 from Eric W. Weisstein, May 04 2006
a(36) = 316872 from Eric W. Weisstein, Feb 04 2007
a(37) = 321874 from Eric W. Weisstein, Feb 19 2007
a(38) = 324098 from Eric W. Weisstein, Feb 25 2007
a(39) = 581132 from Eric W. Weisstein, Feb 15 2011
a(40)-a(42) from Ryan Propper, Jun 19 2022

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A294879 Number of proper divisors of n that are in Perrin sequence, A001608.

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A294880 Number of divisors of n that are in Perrin sequence, A001608.

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PARI

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A112881 Indices of prime Perrin numbers; values of n such that A001608(n) is prime.

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