%I #31 Oct 16 2018 15:27:38

%S 10,69,505,2177,10241,24635,65875,120631,244789,531715,802063,1464941,

%T 2279887,3065943,4444273,6747695,9882205,12447843,17304961,22371177,

%U 26991677,35679165,44240245,56968633,75590451,91181689,104420885,124020811,141249939,164746655

%N Distribute the primes into groups in ascending order, with the n-th group having prime(n) elements. Then a(n) is the sum of the numbers in the n-th group times the number of elements in the group.

%C On every step we sum prime(n) elements from the prime list and multiply the result by the number of elements of the sum.

%H Christian Efrain Maldonado Sifuentes, <a href="/A320228/b320228.txt">Table of n, a(n) for n = 1..297</a>

%F a(n) = A000040(n)*A034958(n). - _Michel Marcus_, Oct 08 2018

%e a(1) = 10 because "sum of next 2 primes times 2" is (2+3)*2;

%e a(2) = 69 because "sum of next 3 primes times 3" is (5+7+11)*3;

%e a(3) = 505 because "sum of next 5 primes times 5" is (13+17+19+23+29)*5;

%e a(4) = 2177 because "sum of next 7 primes times 7" is (31+37+41+43+47+53+59)*7.

%t With[{s = Prime@ Range[10^4]}, Rest@Nest[Append[#, {MapAt[Length[#] Total[#] &, TakeDrop[#[[-1, 1, 2]], Prime@ #[[-1, -1]]], 1], #[[-1, -1]] + 1}] &, {{{{}, s}, 1}}, 30]][[All, 1, 1]] (* _Michael De Vlieger_, Oct 15 2018 *)

%o (PHP)

%o for ($n=1; $i<$maxTestedNumber; $n=$i+1){

%o if(isPrime($n)){

%o while ($amountOfPrimes < $n){

%o if (isPrime($currNum)){

%o $sumPrimes = $sumPrimes + $currNum;

%o $amountOfPrimes++;

%o }

%o $currentNumber=$currentNumber+1;

%o }

%o $sumPrimesTimesN = $n*$sumPrimes;

%o echo "$sumPrimesTimesN, ";

%o $sumPrimes=0; //Reset for next cycle

%o $amountOfPrimes=0; //Reset for next cycle

%o }

%o //isPrime can be any function that returns TRUE if the tested number is prime and FALSE if the tested number is not prime.

%o (PARI) s(n) = sum(k=1, n, prime(k)); \\ A007504

%o f(n) = s(s(n)) - s(s(n-1)); \\ A034958

%o a(n) = prime(n)*f(n); \\ _Michel Marcus_, Oct 12 2018

%Y Cf. A000040, A007504, A034958.

%K nonn,easy

%O 1,1

%A _Christian Efrain Maldonado Sifuentes_, Oct 07 2018