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 A079247 Number of pairs (p,q), 0 <= p < q, such that p+q divides n. 4
 1, 2, 3, 4, 4, 7, 5, 8, 8, 10, 7, 15, 8, 13, 14, 16, 10, 21, 11, 22, 18, 19, 13, 31, 17, 22, 22, 29, 16, 38, 17, 32, 26, 28, 26, 47, 20, 31, 30, 46, 22, 50, 23, 43, 42, 37, 25, 63, 30, 48, 38, 50, 28, 62, 38, 61, 42, 46, 31, 86, 32, 49, 55, 64, 44, 74, 35, 64, 50, 74, 37, 99, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equals left border of triangle A158951. - Gary W. Adamson, Mar 31 2009 Equals row sums of triangle A168509. - Gary W. Adamson, Nov 27 2009 Let c(d_x(n)) = (d_x(n) + 1) / 2 if d_x(n) == 1 (mod 2), and d_x(n) / 2 if d_x(n) == 0 (mod 2), where d_x(n) is the x-th divisor of n, 1 <= d_x(n) <= n, and c(d_x(n)) denotes the cardinality of said divisor within the ordered set of naturals sharing its parity. Then, a(n) = Sum_{i=1..A000005(n)} c(d_i(n)). - Christopher Hohl, Apr 16 2019 LINKS Table of n, a(n) for n=1..73. FORMULA Inverse Moebius transform of A008619 (offset 1). - Michael Somos, Jun 11 2003 G.f.: Sum_{k>=1} x^k / ((1 - x^k) * (1 - x^(2*k))). - Michael Somos, Jun 11 2003 G.f.: Sum_{n>=1} A110654(n)*x^n/(1-x^n). - Mircea Merca, Feb 26 2014 a(n) = (1/2)*(A000203(n) + A001227(n)). - Ridouane Oudra, Sep 06 2020 a(n) = A000203(n) - A086670(n). - Ridouane Oudra, Nov 25 2022 EXAMPLE There are 7 pairs (p,q), 0 <= p < q, such that p+q divides 6: (0,1), (0,2), (0,3), (0,6), (1, 2), (1, 5), (2, 4); thus a(6) = 7. G.f. = x + 2*x^2 + 3*x^3 + 4*x^4 + 4*x^5 + 7*x^6 + 5*x^7 + 8*x^8 + 8*x^9 + ... MAPLE with(numtheory): seq((sigma(n)+tau(2*n)-tau(n))/2, n=1 .. 80); # - Ridouane Oudra, Sep 06 2020 PROG (PARI) {a(n) = if( n<1, 0, sumdiv( n, d, (1 + d)\2))} /* Michael Somos, Jun 11 2003 */ CROSSREFS Cf. A069734, A008619, A158951, A168509, A001227. Cf. A000203, A086670. Sequence in context: A053273 A347700 A049988 * A325588 A244903 A342337 Adjacent sequences: A079244 A079245 A079246 * A079248 A079249 A079250 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 03 2003 STATUS approved

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)