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 A000385 Convolution of A000203 with itself. (Formerly M4113 N1708) 25
 1, 6, 17, 38, 70, 116, 185, 258, 384, 490, 686, 826, 1124, 1292, 1705, 1896, 2491, 2670, 3416, 3680, 4602, 4796, 6110, 6178, 7700, 7980, 9684, 9730, 12156, 11920, 14601, 14752, 17514, 17224, 21395, 20406, 24590, 24556, 28920, 27860, 34112, 32186, 38674, 37994, 43980, 42136, 51646, 47772, 56749, 55500, 64316, 60606, 73420, 67956, 80500, 77760, 88860, 83810, 102284, 92690, 108752, 105236, 120777, 112672, 135120, 123046, 145194, 138656, 157512, 146580, 177515, 159396, 185744, 179122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(5*n+1)==0 (mod 5) and a(7*n+6)==0 (mod 7). See Bonciocat link. - Michel Marcus, Nov 10 2016 Convolution of A340793 and A024916. - Omar E. Pol, Feb 17 2021 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Nicolae Ciprian Bonciocat, Congruences for the Convolution of Divisor sum function, Bull. Greek Math. Soc., p. 19-29, Vol 47, 2003. MathOverflow, Searching for a proof for a series identity S. Ramanujan, On certain arithmetical functions, Transactions of the Cambridge Philosophical Society, 22, No.9 (1916), 169- 184 (see Table IV, line 1). J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39. [Annotated scanned copy] FORMULA a(n) = Sum_{k=1..n} A000203(k)*A000203(n-k+1). G.f.: (1/x)*(Sum_{k>=1} k*x^k/(1 - x^k))^2. - Ilya Gutkovskiy, Nov 10 2016 a(n) = (5/12)*A001158(n+1) - ((5+6*n)/12)*A000203(n+1). - Robert Israel, Sep 17 2018 Sum_{k=1..n} a(k) ~ Pi^4 * n^4 / 864. - Vaclav Kotesovec, Apr 02 2019 MAPLE f:= n -> 5/12*numtheory:-sigma[3](n+1)-(5+6*n)/12*numtheory:-sigma(n+1): map(f, [\$1..100]); # Robert Israel, Sep 17 2018 MATHEMATICA a[n_] := Sum[DivisorSigma[1, k] DivisorSigma[1, n-k+1], {k, 1, n}]; Array[a, 100] (* Jean-François Alcover, Aug 01 2018 *) PROG (Haskell) a000385 n = sum \$ zipWith (*) sigmas \$ reverse sigmas where sigmas = take n a000203_list -- Reinhard Zumkeller, Sep 20 2011 (PARI) a(n) = sum(k=1, n, sigma(k)*sigma(n-k+1)); \\ Michel Marcus, Nov 10 2016 CROSSREFS Cf. A000203, A024916, A001158, A340793. Column k=2 of A319083 (shifted). Sequence in context: A212980 A132127 A023621 * A192756 A004799 A085278 Adjacent sequences: A000382 A000383 A000384 * A000386 A000387 A000388 KEYWORD nonn,easy,look AUTHOR EXTENSIONS More terms from Sean A. Irvine, Nov 14 2010 STATUS approved

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Last modified March 28 05:31 EDT 2023. Contains 361577 sequences. (Running on oeis4.)