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A050449
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a(n) = Sum_{d|n, d==1 (mod 4)} d.
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18
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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
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OFFSET
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1,5
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COMMENTS
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Not multiplicative: a(3)*a(7) != a(21), for example. - R. J. Mathar, Dec 20 2011
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LINKS
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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.
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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a[n_] := DivisorSum[n, Boole[Mod[#, 4] == 1]*#&]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 30 2018 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d*((d % 4) == 1)); \\ Michel Marcus, Jan 30 2018
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CROSSREFS
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Cf. A000593, A050452, A050460, A001826, A035451.
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
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 23 1999
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EXTENSIONS
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More terms from Vladeta Jovovic, Nov 14 2002
More terms from Reinhard Zumkeller, Apr 18 2006
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STATUS
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approved
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