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A370898
Partial alternating sums of the sum of unitary divisors function (A034448).
1
1, -2, 2, -3, 3, -9, -1, -10, 0, -18, -6, -26, -12, -36, -12, -29, -11, -41, -21, -51, -19, -55, -31, -67, -41, -83, -55, -95, -65, -137, -105, -138, -90, -144, -96, -146, -108, -168, -112, -166, -124, -220, -176, -236, -176, -248, -200, -268, -218, -296, -224, -294, -240, -324, -252, -324, -244, -334, -274, -394
OFFSET
1,2
LINKS
László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1.
FORMULA
a(n) = Sum_{k=1..n} (-1)^(k+1) * A034448(k).
a(n) = -c * n^2 + O(n * log(n)^(5/3)), where c = Pi^2/(84*zeta(3)) = 0.0977451984014... (Tóth, 2017).
MATHEMATICA
usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma[1] = 1; Accumulate[Array[(-1)^(# + 1) * usigma[#] &, 100]]
PROG
(PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]); }
lista(kmax) = {my(s = 0); for(k = 1, kmax, s += (-1)^(k+1) * usigma(k); print1(s, ", "))};
CROSSREFS
Similar sequences: A068762, A068773, A307704, A357817, A362028.
Sequence in context: A195952 A236545 A321327 * A370904 A353563 A360250
KEYWORD
sign,easy
AUTHOR
Amiram Eldar, Mar 05 2024
STATUS
approved