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A074787 Sum of squares of the number of unitary divisors of k from 1 to n. 2
1, 5, 9, 13, 17, 33, 37, 41, 45, 61, 65, 81, 85, 101, 117, 121, 125, 141, 145, 161, 177, 193, 197, 213, 217, 233, 237, 253, 257, 321, 325, 329, 345, 361, 377, 393, 397, 413, 429, 445, 449, 513, 517, 533, 549, 565, 569, 585, 589, 605, 621, 637, 641, 657, 673 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
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)).
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
MAPLE
with(numtheory): seq(add(2^(2*nops(ifactors(k)[2])), k=1..n), n=1..100);
MATHEMATICA
Accumulate[Table[Count[Divisors[n], _?(GCD[#, n/#]==1&)], {n, 60}]^2] (* Harvey P. Dale, Dec 06 2012 *)
Accumulate[Table[4^PrimeNu[n], {n, 1, 50}]] (* Amiram Eldar, Jul 02 2022 *)
CROSSREFS
Equals 4*A069811(n) + 1, for n <= 29.
Sequence in context: A349538 A334524 A125018 * A255645 A079497 A314701
KEYWORD
nonn
AUTHOR
Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
STATUS
approved

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Last modified February 29 04:26 EST 2024. Contains 370401 sequences. (Running on oeis4.)