cp's OEIS Frontend

A074787 Sum of squares of the number of unitary divisors of k from 1 to n.

%I A074787 #10 Jul 02 2022 05:58:55
%S A074787 1,5,9,13,17,33,37,41,45,61,65,81,85,101,117,121,125,141,145,161,177,
%T A074787 193,197,213,217,233,237,253,257,321,325,329,345,361,377,393,397,413,
%U A074787 429,445,449,513,517,533,549,565,569,585,589,605,621,637,641,657,673
%N A074787 Sum of squares of the number of unitary divisors of k from 1 to n.
%H A074787 Harvey P. Dale, <a href="/A074787/b074787.txt">Table of n, a(n) for n = 1..1000</a>
%F A074787 a(n) = Sum_{k=1..n} ud(k)^2 = Sum_{k=1..n} A034444(k)^2 . a(n) = Sum_{k=1..n} 2^(2*omega(k)) = Sum_{k=1..n} 2^(2*A001221(k)).
%F A074787 a(n) ~ c * n * log(n)^3, where c = (1/6) * Product_{p prime} ((1-1/p)^3*(1+3/p)) = A319592 / 6. - _Amiram Eldar_, Jul 02 2022
%p A074787 with(numtheory): seq(add(2^(2*nops(ifactors(k)[2])),k=1..n),n=1..100);
%t A074787 Accumulate[Table[Count[Divisors[n],_?(GCD[#,n/#]==1&)],{n,60}]^2] (* _Harvey P. Dale_, Dec 06 2012 *)
%t A074787 Accumulate[Table[4^PrimeNu[n], {n, 1, 50}]] (* _Amiram Eldar_, Jul 02 2022 *)
%Y A074787 Cf. A034444, A064608, A069212, A285052, A319592.
%Y A074787 Equals 4*A069811(n) + 1, for n <= 29.
%K A074787 nonn
%O A074787 1,2
%A A074787 Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002