|
Search: id:A050999
|
|
|
| A050999 |
|
Sum of squares of odd divisors of n. |
|
+0
9
|
|
| 1, 1, 10, 1, 26, 10, 50, 1, 91, 26, 122, 10, 170, 50, 260, 1, 290, 91, 362, 26, 500, 122, 530, 10, 651, 170, 820, 50, 842, 260, 962, 1, 1220, 290, 1300, 91, 1370, 362, 1700, 26, 1682, 500, 1850, 122, 2366, 530, 2210, 10, 2451, 651
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
FORMULA
|
Multiplicative with a(p^e) = 1 if p = 2, (p^(2e+2)-1)/(p^2-1) if p > 2. a(n) = 1/2*Sum_{d|n} ((1-(-1)^d)*d^2. a(2n)=sigma_2(2n)-4*sigma_2(n), a(2n+1)=sigma_2(2n+1), where sigma_2(n) is sum of squares of divisors of n (A001157). More generally, if b(n, k) is sum of k-th powers of odd divisors of n then b(2n, k) = sigma_k(2n)-2^k*sigma_k(n), b(2n+1, k) =sigma_k(2n+1). b(n, k) is multiplicative with a(p^e) = 1 if p = 2, (p^(ke+k)-1)/(p^k-1) if p > 2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 10 2001
G.f. for b(n, k): Sum_{m>0} m^k*x^m*(1-(2^k-1)*x^m)/(1-x^(2*m)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 19 2002
|
|
CROSSREFS
|
Cf. A051000, A051001, A051002, A000593, A001227, A000203, A001157-A001160, A013954-A013972.
Sequence in context: A040109 A036188 A013617 this_sequence A070246 A085044 A059022
Adjacent sequences: A050996 A050997 A050998 this_sequence A051000 A051001 A051002
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
Eric Weisstein (eric(AT)weisstein.com)
|
|
|
Search completed in 0.002 seconds
|
