A343548
a(n) = Sum_{d|n} binomial(d+n-1,n).
Original entry on oeis.org
1, 4, 11, 41, 127, 498, 1717, 6610, 24366, 93391, 352717, 1358826, 5200301, 20097076, 77562773, 300786339, 1166803111, 4539163784, 17672631901, 68933291834, 269129233484, 1052113994124, 4116715363801, 16124221819056, 63205303242628, 247961973949228, 973469736360283
Offset: 1
-
a[n_] := DivisorSum[n, Binomial[# + n - 1, n] &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)
-
a(n) = sumdiv(n, d, binomial(d+n-1, n));
A343565
a(n) = |{(x_1, x_2, ... , x_n) : 1 <= x_1 <= x_2 <= ... <= x_n <= n, gcd(x_1, x_2, ... , x_n, n) = 1}|.
Original entry on oeis.org
1, 2, 9, 30, 125, 428, 1715, 6270, 24255, 91367, 352715, 1345448, 5200299, 20019526, 77554749, 300295038, 1166803109, 4535971916, 17672631899, 68913247655, 269128640958, 1051984969598, 4116715363799, 16123381989000, 63205303195125, 247956558998878, 973469689288236
Offset: 1
-
a[n_] := DivisorSum[n, MoebiusMu[n/#] * Binomial[# + n - 1, n] &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)
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a(n) = sumdiv(n, d, moebius(n/d)*binomial(d+n-1, n));
A343568
a(n) = Sum_{d|n} (n/d)^(n/d) * binomial(d+n-1,n).
Original entry on oeis.org
1, 7, 37, 311, 3251, 47419, 825259, 16786615, 387446284, 10000130757, 285312023327, 8916102467195, 302875111792553, 11112006858124501, 437893890458947787, 18446744074296533175, 827240261887503567287, 39346408075308452154628
Offset: 1
-
a[n_] := DivisorSum[n, (n/#)^(n/#) * Binomial[# + n - 1, n] &]; Array[a, 20] (* Amiram Eldar, Apr 25 2021 *)
-
a(n) = sumdiv(n, d, (n/d)^(n/d)*binomial(d+n-1, n));
A363660
a(n) = Sum_{d|n} binomial(d+n,n).
Original entry on oeis.org
2, 9, 24, 90, 258, 1043, 3440, 13419, 48850, 187836, 705444, 2725099, 10400614, 40233015, 155133856, 601820876, 2333606238, 9079958260, 35345263820, 137876637843, 538259060526, 2104292500739, 8233430727624, 32248866496625, 126410606580284
Offset: 1
-
a[n_] := DivisorSum[n, Binomial[# + n, n] &]; Array[a, 25] (* Amiram Eldar, Jul 17 2023 *)
-
a(n) = sumdiv(n, d, binomial(d+n, n));
A363668
a(n) = Sum_{d|n} (n/d)^d * binomial(d+n-1,d).
Original entry on oeis.org
1, 7, 19, 91, 151, 1135, 1765, 12355, 28846, 157917, 352837, 2280955, 5200469, 29986201, 80469589, 427061795, 1166803399, 6211188028, 17672632261, 89483074521, 271071666724, 1316291647997, 4116715364329, 19595444140771, 63205674328876, 292318539358879
Offset: 1
-
a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n - 1, #] &]; Array[a, 30] (* Amiram Eldar, Jul 12 2023 *)
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a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n-1, d));
A363669
a(n) = Sum_{d|n} (n/d)^n * binomial(d+n-1,d).
Original entry on oeis.org
1, 11, 91, 1219, 15751, 299291, 5766517, 136667939, 3490056406, 100539251801, 3138428729437, 107169878769043, 3937376390899589, 155639310270607349, 6568429274592664981, 295186202455912472867, 14063084452068891794119, 708261127356256620907496
Offset: 1
-
a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + n - 1, #] &]; Array[a, 20] (* Amiram Eldar, Jul 12 2023 *)
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a(n) = sumdiv(n, d, (n/d)^n*binomial(d+n-1, d));
Showing 1-6 of 6 results.