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%I #41 Feb 16 2024 10:09:39
%S 0,0,0,1,1,3,1,4,6,7,4,8,8,13,10,8,12,18,20,27,28,26,21,29,33,37,31,
%T 37,37,46,46,56,65,62,54,53,59,70,61,57,62,74,75,88,89,95,84,98,108,
%U 116,124,119,119,134,145,145,152,146,131,147,154,171,156,164,180,180,182,200,200,193,198,217
%N Sum of remainders n mod p, over all primes p < n.
%H Alois P. Heinz, <a href="/A024934/b024934.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = n*A000720(n) - A024924(n). - _Max Alekseyev_, Feb 10 2012
%F a(n) = a(n-1) + A000720(n-1) - A105221(n). - _Max Alekseyev_, Nov 28 2017
%e a(5) = 3. The remainder when 5 is divided by primes 2, 3 respectively is 1, 2, and their sum = 3.
%e 10 = 2*5+0 = 3*3+1 = 5*2+0 = 7*1+3: a(10) = 0+1+0+3 = 4.
%t a[n_] := Sum[Mod[n, Prime[i]], {i, PrimePi@ n}]; Array[a, 72, 0] (* _Giovanni Resta_, Jun 24 2016 *)
%o (PARI) a(n)=my(r=0);forprime(p=2,n,r+=n%p); r; \\ _Joerg Arndt_, Nov 05 2016
%Y Cf. A004125, A067435, A067436, A013939, A101336.
%K nonn
%O 0,6
%A _Clark Kimberling_
%E Edited by _Max Alekseyev_, Jan 30 2012
%E a(0)=0 prepended by _Max Alekseyev_, Dec 10 2013
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