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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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8
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1, 87, 8299, 823081, 82256014, 8224740835, 822468118437, 82246711794796, 8224670422194237, 822467034112360628, 82246703352400266400, 8224670334323560419029, 822467033425357340138978
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| S. A. Troisi, Table of n, a(n) for n=1..24 [This replaces an earlier b-file computed by P. L. Patodia]]
P. L. Patodia (pannalal(AT)usa.net), PARI program for A072692 and A024916
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FORMULA
| 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
| 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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PROG
| (PARI) for(m=0, 10, k=10^m; s=0; for(n=1, k, s=s+n*(k\n)); print1(s, ", "))
(Python) [(i, sum([d*(10**i//d) for d in xrange(1, 10**i+1)])) for i in xrange(8)] [From Seth Troisi (braintwo+math(AT)gmail.com), Jun 27 2010]
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CROSSREFS
| 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: A017803 A017750 A183040 * A133391 A033408 A109989
Adjacent sequences: A072689 A072690 A072691 * A072693 A072694 A072695
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 02 2002
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EXTENSIONS
| 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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