A070921 - OEIS

%I #35 Sep 03 2023 08:44:56

%S 1,31,31,211,31,961,31,781,211,961,31,6541,31,961,961,2101,31,6541,31,

%T 6541,961,961,31,24211,211,961,781,6541,31,29791,31,4651,961,961,961,

%U 44521,31,961,961,24211,31,29791,31,6541,6541,961,31,65131,211,6541

%N a(n) = Card{ (x,y,z,u,v) | lcm(x,y,z,u,v)=n }.

%C A048691(n) gives Card{ (x,y) | lcm(x,y)=n }.

%H Antti Karttunen, <a href="/A070921/b070921.txt">Table of n, a(n) for n = 1..10000</a>

%H O. Bagdasar, <a href="https://doi.org/10.5937/SPSUNP1402091B">On some functions involving the lcm and gcd of integer tuples</a>, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91-100.

%F a(n) = Sum_{d|n} A000005(d)^5*A008683(n/d).

%F Sum_{k>0} a(k)/k^s = (1/zeta(s))*Sum_{k>0} tau(k)^5/k^s.

%F Multiplicative with a(p^e) = (e+1)^5 - e^5. - _Amiram Eldar_, Sep 03 2023

%t Join[{1},Table[Product[(k + 1)^5 - k^5, {k, FactorInteger[n][[All, 2]]}], {n,2, 68}]] (* _Geoffrey Critzer_, Jan 10 2015 *)

%o (PARI) for(n=1,100,print1(sumdiv(n,d,numdiv(d)^5*moebius(n/d)),","))

%o (PARI) a(n) = vecprod(apply(x->(x+1)^5-x^5, factor(n)[, 2])); \\ _Amiram Eldar_, Sep 03 2023

%Y Cf. A000005, A008683, A048691, A070919, A070920, A247517 (Mobius transform).

%K mult,easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 20 2002