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 A078392 Sum of GCD's of parts in all partitions of n. 13
 1, 3, 5, 9, 11, 20, 21, 35, 42, 61, 66, 112, 113, 168, 210, 279, 313, 461, 508, 719, 852, 1088, 1277, 1756, 2006, 2573, 3106, 3937, 4593, 5958, 6872, 8676, 10305, 12655, 15009, 18664, 21673, 26559, 31447, 38217, 44623, 54386, 63303, 76379, 89696, 106879 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equals row sums of triangle A168534. - Gary W. Adamson, Nov 28 2009 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA a(n) = Sum_{d|n} d * A000837(n/d). a(n) = Sum_{d|n} phi(n/d)*numbpart(d) = Sum_{d|n} A000010(n/d)*A000041(d). - Vladeta Jovovic, May 08 2003 EXAMPLE Partitions of 4 are 1+1+1+1, 1+1+2, 2+2, 1+3, 4, the corresponding GCD's of parts are 1,1,2,1,4 and their sum is a(4) = 9. MAPLE with(numtheory): with(combinat): a:= n-> add(phi(n/d)*numbpart(d), d=divisors(n)): seq(a(n), n=1..50);  # Alois P. Heinz, Apr 02 2015 MATHEMATICA a[n_] := Sum[EulerPhi[n/d]*PartitionsP[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 01 2015, after Alois P. Heinz *) CROSSREFS Cf. A168534, A181844 (the same for LCM), A319301. Sequence in context: A282098 A034760 A070639 * A187753 A231716 A113488 Adjacent sequences:  A078389 A078390 A078391 * A078393 A078394 A078395 KEYWORD nonn AUTHOR Vladeta Jovovic, Dec 24 2002 STATUS approved

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Last modified August 8 02:22 EDT 2020. Contains 336290 sequences. (Running on oeis4.)