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 A243076 Let f(p,i) = smallest m > p such that m == i mod p; a(n) = Sum_{i=0..p-1) f(p,i), where p = n-th prime. 1
 5, 15, 55, 119, 341, 533, 901, 1387, 1909, 3103, 4061, 5365, 6601, 7783, 9635, 12455, 16343, 17507, 20033, 24069, 27083, 29941, 33283, 42453, 47433, 53631, 54693, 60241, 66163, 69721, 86741, 92879, 104805, 102443, 126203, 130011, 136119, 143603, 157147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is always odd. From Robert G. Wilson v, Jun 21 2017: (Start) Obviously, prime(n)|a(n) for n>1. a(n)/prime(n), n>1: 5, 11, 17, 31, 41, 53, 73, 83, 107, 131, 145, 161, 181, 205, 235, 277, 287, 299, 339, etc. Values of n such that a(n) < a(n-1): 34, 51, 57, 58, 65, 69, 71, 91, 96, 105, 109, 111, .... (End) LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 EXAMPLE a(1) = 5 = 2+3, a(2) = 15 = 3+7+5, a(3) = 55 = 5+11+7+13+19, a(4) = 119 = 7+29+23+17+11+19+13, a(5) = 341 = 11+23+13+47+37+71+17+29+19+31+43, etc. MATHEMATICA f[n_] := Block[{p = Prime@ n, q, i = s = 0}, While[i < p, q = If[OddQ@ i, 2, 1]*p + i; While[ !PrimeQ@ q, q += 2p]; s += q; i++]; s]; f[1] = 5; Array[f, 100] (* Robert G. Wilson v, Jun 21 2017 *) PROG (PARI) a(n) = {res = 0; for (index = 0, prime(n)-1, m = n; while ((prime(m) % prime(n)) != index, m++; ); res += prime(m); ); res; } \\ Michel Marcus, Jun 04 2014 (Python) from sympy import prime, isprime def a(n):     if n==1: return 5     p=prime(n)     i=0     s=0     while i

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)