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.

A056190 a(n) = Sum_{d|n and gcd(d, n/d)=1} binomial(n,d).

This page as a plain text file.
%I A056190 #17 Jul 28 2024 03:36:07
%S A056190 1,3,4,5,6,42,8,9,10,308,12,728,14,3538,3474,17,18,48792,20,20370,
%T A056190 117632,705686,24,737520,26,10400952,28,1204544,30,185903342,32,33,
%U A056190 193542210,2333606816,7049188,94202222,38,35345264542,8122434623
%N A056190 a(n) = Sum_{d|n and gcd(d, n/d)=1} binomial(n,d).
%H A056190 Alois P. Heinz, <a href="/A056190/b056190.txt">Table of n, a(n) for n = 1..3000</a>
%F A056190 a(n) = A056045(n) for squarefree n, when all divisors are unitary.
%e A056190 n=100 has 9 divisors of which {1,4,25,100} are unitary, so a(100) = 100 + 3921225 + 242519269720337121015504 + 1.
%p A056190 a:= n-> add(`if`(igcd(d, n/d)=1, binomial(n, d), 0),
%p A056190                       d=numtheory[divisors](n)):
%p A056190 seq(a(n), n=1..40);  # _Alois P. Heinz_, Aug 25 2019
%t A056190 a[n_] := Total[Binomial[n, Select[Divisors[n], CoprimeQ[#, n/#] &]]]; Array[a, 40] (* _Amiram Eldar_, Jul 28 2024 *)
%o A056190 (PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d)==1, binomial(n, d))); \\ _Michel Marcus_, Aug 25 2019
%Y A056190 Cf. A056045.
%K A056190 nonn
%O A056190 1,2
%A A056190 _Labos Elemer_, Aug 02 2000