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.
%I A141056 #48 Feb 18 2022 23:08:49 %S A141056 1,2,6,2,30,2,42,2,30,2,66,2,2730,2,6,2,510,2,798,2,330,2,138,2,2730, %T A141056 2,6,2,870,2,14322,2,510,2,6,2,1919190,2,6,2,13530,2,1806,2,690,2,282, %U A141056 2,46410,2,66,2,1590,2,798,2,870,2,354,2,56786730,2,6,2,510,2,64722,2,30,2,4686 %N A141056 1 followed by A027760, a variant of Bernoulli number denominators. %C A141056 The denominators of the Bernoulli numbers for n>0. B_n sequence begins 1, -1/2, 1/6, 0/2, -1/30, 0/2, 1/42, 0/2, ... This is an alternative version of A027642 suggested by the theorem of Clausen. - _Peter Luschny_, Apr 29 2009 %C A141056 Let f(n,k) = gcd { multinomial(n; n1, ..., nk) | n1 + ... + nk = n }; then a(n) = f(N,N-n+1)/f(N,N-n) for N >> n. - _Mamuka Jibladze_, Mar 07 2017 %H A141056 Antti Karttunen, <a href="/A141056/b141056.txt">Table of n, a(n) for n = 0..10080</a> %H A141056 Thomas Clausen, <a href="http://adsabs.harvard.edu/abs/1840AN.....17R.351">Lehrsatz aus einer Abhandlung Über die Bernoullischen Zahlen</a>, Astr. Nachr. 17 (22) (1840), 351-352. %H A141056 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bernoulli_number">Bernoulli number</a> %F A141056 a(n) are the denominators of the polynomials generated by cosh(x*z)*z/(1-exp(-z)) evaluated x=1. See A176328 for the numerators. - _Peter Luschny_, Aug 18 2018 %F A141056 a(n) = denominator(Sum_{j=0..n} (-1)^(n-j)*j!*Stirling2(n,j)*B(j)), where B are the Bernoulli numbers A164555/A027642. - _Fabián Pereyra_, Jan 06 2022 %e A141056 The rational values as given by the e.g.f. in the formula section start: 1, 1/2, 7/6, 3/2, 59/30, 5/2, 127/42, 7/2, 119/30, ... - _Peter Luschny_, Aug 18 2018 %p A141056 Clausen := proc(n) local S,i; %p A141056 S := numtheory[divisors](n); S := map(i->i+1,S); %p A141056 S := select(isprime,S); mul(i,i=S) end proc: %p A141056 seq(Clausen(i),i=0..24); %p A141056 # _Peter Luschny_, Apr 29 2009 %p A141056 A141056 := proc(n) %p A141056 if n = 0 then 1 else A027760(n) end if; %p A141056 end proc: # _R. J. Mathar_, Oct 28 2013 %t A141056 a[n_] := Sum[ Boole[ PrimeQ[d+1]] / (d+1), {d, Divisors[n]}] // Denominator; Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Aug 09 2012 *) %o A141056 (PARI) %o A141056 A141056(n) = %o A141056 { %o A141056 p = 1; %o A141056 if (n > 0, %o A141056 fordiv(n, d, %o A141056 r = d + 1; %o A141056 if (isprime(r), p = p*r) %o A141056 ) %o A141056 ); %o A141056 return(p) %o A141056 } %o A141056 for(n=0,70,print1(A141056(n), ", ")); /* _Peter Luschny_, May 07 2012 */ %Y A141056 Cf. A027760, A027642, A176328. %Y A141056 Cf. A164555, A027642, A048993. %K A141056 nonn %O A141056 0,2 %A A141056 _Paul Curtz_, Aug 01 2008 %E A141056 Extended by _R. J. Mathar_, Nov 22 2009