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Search: id:A076577
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| A076577 |
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Sum of squares of divisors d of n such that n/d is odd. |
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+0
3
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| 1, 4, 10, 16, 26, 40, 50, 64, 91, 104, 122, 160, 170, 200, 260, 256, 290, 364, 362, 416, 500, 488, 530, 640, 651, 680, 820, 800, 842, 1040, 962, 1024, 1220, 1160, 1300, 1456, 1370, 1448, 1700, 1664, 1682, 2000, 1850, 1952, 2366, 2120, 2210, 2560, 2451, 2604
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OFFSET
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1,2
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FORMULA
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G.f.: Sum_{m>0} m^2*x^m/(1-x^(2*m)). More generally, if b(n, k) is sum of k-th powers of divisors d of n such that n/d is odd then b(2n, k) = sigma_k(2n)-sigma_k(n), b(2n+1, k) =sigma_k(2n+1), where sigma_k(n) is sum of k-th powers of divisors of n. G.f. for b(n, k): Sum_{m>0} m^k*x^m/(1-x^(2*m)).
b(n, k) is multiplicative: b(2^e, k) = 2^(k*e), b(p^e, k) = (p^(ke+k)-1)/(p^k-1) for an odd prime p.
a(2*n) = sigma_2(2*n)-sigma_2(n), a(2*n+1) = sigma_2(2*n+1), where sigma_2(n) is sum of squares of divisors of n (cf. A001157).
b(n, k) = (sigma_k(2n)-sigma_k(n))/2^k. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 06 2003
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CROSSREFS
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Cf. A001227, A002131, A001157, A050999.
Sequence in context: A054901 A019574 A095273 this_sequence A008148 A089340 A132227
Adjacent sequences: A076574 A076575 A076576 this_sequence A076578 A076579 A076580
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KEYWORD
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mult,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2002
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