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Search: id:A072692
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| A072692 |
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Sum of sigma(j) for 1<=j<=10^n, where sigma(j) is the sum of the divisors of j. |
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+0
6
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| 1, 87, 8299, 823081, 82256014, 8224740835, 822468118437, 82246711794796, 8224670422194237, 822467034112360628, 82246703352400266400, 8224670334323560419029, 822467033425357340138978
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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P. L. Patodia (pannalal(AT)usa.net), Table of n, a(n) for n = 0..18
P. L. Patodia (pannalal(AT)usa.net), PARI program for A072692 and A024916
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FORMULA
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Asymptotic formula: a(n) ~ Pi^2/12 * 10^2n. See A072691 for Pi^2/12. Observe that A025281 also contains that constant in its asymptotic formula.
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EXAMPLE
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For n=1, the sum of sigma(j) for j<=10 is 1+3+4+7+6+12+8+15+13+18=87, so a(1)=87 (=69+18=A049000(1)+A046915(1)).
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PROGRAM
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(PARI) for(m=0, 10, k=10^m; s=0; for(n=1, k, s=s+n*(k\n)); print1(s, ", "))
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CROSSREFS
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Compare with A049000. Note that A072692(n) = A049000(n) + A046915(n).
Cf. A000203 (sigma(n)), A072691 (Pi^2/12), A049000, A046915, A024916, A025281.
Sequence in context: A116269 A017803 A017750 this_sequence A133391 A033408 A109989
Adjacent sequences: A072689 A072690 A072691 this_sequence A072693 A072694 A072695
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 02 2002
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EXTENSIONS
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More terms from P L Patodia (pannalal(AT)usa.net), Jan 11 2008, Jun 25 2008
Corrected by N. J. A. Sloane (njas(AT)research.att.com), Jun 08 2008, following suggestions from Don Reble and David Wilson.
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