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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 Seiichi Manyama, Table of n, a(n) for n = 1..10000 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. A000593, A050452, A050460, A001826, A035451, A245058. 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 Adjacent sequences: A050446 A050447 A050448 * A050450 A050451 A050452 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.)