Displaying 31-40 of 49 results found.
a(n) = n*Product_{p prime, p|n} (p - 1)/2.
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1, 1, 3, 2, 10, 3, 21, 4, 9, 10, 55, 6, 78, 21, 30, 8, 136, 9, 171, 20, 63, 55, 253, 12, 50, 78, 27, 42, 406, 30, 465, 16, 165, 136, 210, 18, 666, 171, 234, 40, 820, 63, 903, 110, 90, 253, 1081, 24, 147, 50, 408, 156, 1378, 27, 550, 84, 513, 406, 1711, 60, 1830, 465, 189
p(p+1)(2p+1) where p is prime.
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30, 84, 330, 840, 3036, 4914, 10710, 14820, 25944, 51330, 62496, 105450, 142926, 164604, 214320, 306234, 421260, 465186, 615060, 731016, 794094, 1004880, 1164324, 1433790, 1853670, 2091306, 2217384, 2484540, 2625810, 2924214
Prime partial sums of pentagonal numbers with prime indices.
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5, 17, 4957, 129277, 2826443, 3861083, 5126483, 9451573, 19811083, 53751743, 68136617, 98729003, 264616831, 388771421, 498157871, 608312141, 682548511, 779346653, 918754301, 1174179079, 1700023891, 2056298683, 2149703411
a(n) = T(p(n)) - p(T(n)) = Commutator[triangular numbers, primes] at n.
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1, 1, 2, -1, 19, 18, 46, 39, 79, 178, 179, 306, 394, 375, 469, 662, 887, 872, 1127, 1265, 1248, 1553, 1703, 2018, 2600, 2780, 2763, 2987, 2958, 3134, 4587, 4849, 5380, 5373, 6518, 6503, 7100, 7725, 8089, 8750, 9431, 9452, 10859, 10892, 11260, 11219, 13275, 15485, 15947, 15908, 16358, 17257, 17222, 19189
3, 6, 15, 28, 91, 153, 190, 496, 1891, 4005, 5778, 8128, 135981, 184528, 818560, 2427706, 2602621, 5176153, 9046131, 9783676, 46943205, 49416711, 62871291, 198751953, 235477551, 269340445, 990013753, 3718970646, 6105511756, 8718535225, 23347768186, 286403014380
Triangular numbers n*(n+1)/2 with n prime and n+1 nonprime.
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6, 15, 28, 66, 91, 153, 190, 276, 435, 496, 703, 861, 946, 1128, 1431, 1770, 1891, 2278, 2556, 2701, 3160, 3486, 4005, 4753, 5151, 5356, 5778, 5995, 6441, 8128, 8646, 9453, 9730, 11175, 11476, 12403, 13366, 14028, 15051, 16110, 16471, 18336, 18721, 19503, 19900, 22366, 24976, 25878
a(n) is the number of positive integers of the form (n-3k)/(2k+1), 1 <= k <= (n-1)/5.
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0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 3, 0, 1, 1, 0, 2, 1, 0, 0, 3, 2, 0, 1, 0, 0, 3, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2, 0, 3, 0, 0, 5, 0, 0, 1, 0, 2, 3, 2, 1, 1, 2, 0, 1, 0, 2, 5, 0, 0, 1, 2, 2, 3, 0, 0, 3, 2, 0, 1, 2, 0, 5, 0, 1, 3, 0, 4, 1, 0, 0, 1
a(n) is the number of nontrivial positive divisors of 2n+3.
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0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 1, 2, 0, 2, 2, 0, 0, 4, 2, 0, 2, 0, 0, 4, 2, 0, 3, 0, 2, 2, 0, 2, 2, 2, 0, 4, 0, 0, 6, 0, 0, 2, 0, 2, 4, 2, 1, 2, 2, 0, 2, 0, 2, 6, 0, 0, 2, 2, 2, 4, 0, 0, 4, 2, 0, 2, 2, 0, 6, 0, 1, 4, 0, 4, 2, 0, 0, 2
Sum of all numbers from n to n-th prime.
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3, 5, 12, 22, 56, 76, 132, 162, 240, 390, 441, 637, 783, 855, 1023, 1311, 1634, 1738, 2107, 2366, 2491, 2929, 3233, 3729, 4453, 4826, 5005, 5400, 5589, 6006, 7663, 8150, 8925, 9169, 10580, 10846, 11737, 12663, 13287, 14271, 15290, 15610, 17433, 17775
Least prime p such that f(0),...,f(n) are all primes, where f(0) = p, then f(i+1) = triangular(f(i))+1.
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3, 3, 43, 236367611, 31542795419
COMMENTS
Triangular(p) = p*(p+1)/2 (see A034953).
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