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 A062020 a(n) = Sum_{i=1..n} Sum_{j=1..i} (prime(i) - prime(j)). 6
 0, 1, 6, 17, 44, 81, 142, 217, 324, 485, 666, 913, 1208, 1529, 1906, 2373, 2936, 3533, 4238, 5019, 5840, 6787, 7822, 8995, 10360, 11825, 13342, 14967, 16648, 18445, 20662, 23003, 25536, 28135, 31074, 34083, 37308, 40755, 44354, 48187, 52260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA a(n) = a(n-1) + n*prime(n) - Sum_{i = 1..n} prime(i), with a(0) = 0. a(n) = 2*a(n-1) - a(n-2) + (n-1)*(prime(n) - prime(n-1)), with a(1) = 0, a(2) = 1. a(n) = Sum_{j=1..n} (2*j - (n+1))*prime(j) = 2*A014285(n) - (n+1)*A007504(n). - G. C. Greubel, May 04 2022 EXAMPLE a(3) = (5-2) + (5-3) + (3-2) = 6. MATHEMATICA a[n_]:= a[n]= If[n<3, (n-1), 2*a[n-1] -a[n-2] +(n-1)*(Prime[n] -Prime[n-1])]; Table[a[n], {n, 50}] (* G. C. Greubel, May 04 2022 *) PROG (SageMath) @CachedFunction def a(n): # A062020 if (n<3): return (n-1) else: return 2*a(n-1) - a(n-2) + (n-1)*(nth_prime(n) - nth_prime(n-1)) [a(n) for n in (1..50)] # G. C. Greubel, May 04 2022 CROSSREFS Cf. A000040, A007504, A014285, A062021, A062022. Sequence in context: A171507 A099858 A232567 * A066183 A262297 A048746 Adjacent sequences: A062017 A062018 A062019 * A062021 A062022 A062023 KEYWORD nonn AUTHOR Amarnath Murthy, Jun 02 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Jun 05 2001 Name edited by G. C. Greubel, May 04 2022 STATUS approved

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Last modified November 29 16:32 EST 2022. Contains 358431 sequences. (Running on oeis4.)