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A050449 a(n) = Sum_{d|n, d == 1 (mod 4)} d. 24
1, 1, 1, 1, 6, 1, 1, 1, 10, 6, 1, 1, 14, 1, 6, 1, 18, 10, 1, 6, 22, 1, 1, 1, 31, 14, 10, 1, 30, 6, 1, 1, 34, 18, 6, 10, 38, 1, 14, 6, 42, 22, 1, 1, 60, 1, 1, 1, 50, 31, 18, 14, 54, 10, 6, 1, 58, 30, 1, 6, 62, 1, 31, 1, 84, 34, 1, 18, 70, 6, 1, 10, 74, 38, 31, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Not multiplicative: a(3)*a(7) != a(21), for example. - R. J. Mathar, Dec 20 2011
LINKS
Mariusz Skałba, A Note on Sums of Two Squares and Sum-of-divisors Functions, INTEGERS 20A (2020) A92.
FORMULA
G.f.: Sum_{n>=0} (4*n+1)*x^(4*n+1)/(1-x^(4*n+1)). - Vladeta Jovovic, Nov 14 2002
a(n) = A000593(n) - A050452(n). - Reinhard Zumkeller, Apr 18 2006
G.f.: Sum_{n >= 1} x^n*(1 + 3*x^(4*n))/(1 - x^(4*n))^2. - Peter Bala, Dec 19 2021
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/48 = 0.205616... (A245058). - Amiram Eldar, Nov 26 2023
MAPLE
A050449 := proc(n)
a := 0 ;
for d in numtheory[divisors](n) do
if d mod 4 = 1 then
a := a+d ;
end if;
end do:
a;
end proc:
seq(A050449(n), n=1..40) ; # R. J. Mathar, Dec 20 2011
MATHEMATICA
a[n_] := DivisorSum[n, Boole[Mod[#, 4] == 1]*#&]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 30 2018 *)
PROG
(PARI) a(n) = sumdiv(n, d, d*((d % 4) == 1)); \\ Michel Marcus, Jan 30 2018
CROSSREFS
Cf. Sum_{d|n, d==1 (mod k)} d: A000593 (k=2), A078181 (k=3), this sequence (k=4), A284097 (k=5), A284098 (k=6), A284099 (k=7), A284100 (k=8).
Sequence in context: A304404 A290480 A183092 * A316623 A108131 A073354
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 23 1999
EXTENSIONS
More terms from Vladeta Jovovic, Nov 14 2002
More terms from Reinhard Zumkeller, Apr 18 2006
STATUS
approved

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Last modified April 20 05:25 EDT 2024. Contains 371798 sequences. (Running on oeis4.)