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Sum of all numbers from n to n-th prime.
1

%I #11 Sep 08 2022 08:45:45

%S 3,5,12,22,56,76,132,162,240,390,441,637,783,855,1023,1311,1634,1738,

%T 2107,2366,2491,2929,3233,3729,4453,4826,5005,5400,5589,6006,7663,

%U 8150,8925,9169,10580,10846,11737,12663,13287,14271,15290,15610,17433,17775

%N Sum of all numbers from n to n-th prime.

%H Harvey P. Dale, <a href="/A161624/b161624.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = Sum_{k=n..prime(n)} k.

%F a(n) = A034953(n) - A000217(n-1). - _Michel Marcus_, Feb 02 2018

%e First prime is 2, so a(1) = 1+2 = 3; fifth prime is 11, so a(5) = 5+6+7+8+9+10+11 = 56.

%t snos[n_]:=Module[{pr=Prime[n]},((pr+n)(pr-n+1))/2]; Array[snos, 50] (* _Harvey P. Dale_, Jun 05 2012 *)

%o (Magma) [ &+[n..NthPrime(n)]: n in [1..44] ]; // _Klaus Brockhaus_, Jun 14 2009

%Y Cf. A000027, A000040, A000217, A034953, A161570.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jun 15 2009

%E Edited and extended by _Klaus Brockhaus_, Jun 15 2009