%I #56 Jun 16 2024 08:44:10

%S 4,21,75,189,495,897,1683,2565,4071,6641,8959,13209,17835,22317,28623,

%T 37577,48439,57401,71623,85697,98623,118737,138195,163493,196231,

%U 224321,249775,281945,310759,347249,420751,467801,525943,571985,656047

%N Divide odd numbers into groups with prime(n) elements and add together.

%H Hieronymus Fischer, <a href="/A034960/b034960.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Hieronymus Fischer_, Sep 26 2012: (Start)

%F a(n) = Sum_{k=A007504(n-1)+1..A007504(n)} (2*k-1).

%F a(n) = A007504(n)^2 - A007504(n-1)^2.

%F a(n) = 2*A034957(n) + A000040(n).

%F a(n) = 2*A034956(n) - A000040(n).

%F a(n) = A034959(n) + A000040(n). (End)

%F a(n) = A061802(n)*A000040(n). - _Marco Zárate_, May 12 2023

%e {1,3} #2 S=4;

%e {5,7,9} #3 S=21;

%e {11,13,15,17,19} #5 S=75;

%e {21,23,25,27,29,31,33} #7 S=189.

%p S:= n-> sum(ithprime(k), k=1..n): seq(S(n+1)^2-S(n)^2, n=0..40); # _Gary Detlefs_, Dec 20 2011

%o (Python)

%o from itertools import islice

%o from sympy import nextprime

%o def A034960_gen(): # generator of terms

%o a, p = 0, 2

%o while True:

%o yield p*((a<<1)+p)

%o a, p = a+p, nextprime(p)

%o A034960_list = list(islice(A034960_gen(),20)) # _Chai Wah Wu_, Mar 22 2023

%o (PARI) a0(n) = vecsum(primes(n))^2 - vecsum(primes(n-1))^2; \\ _Michel Marcus_, Jun 16 2024

%Y Cf. A006003, A027441, A034959.

%Y Cf. A007504.

%Y Cf. A000040, A034956, A034957, A034958, A046992, A061802.

%K nonn

%O 1,1

%A _Patrick De Geest_, Oct 15 1998