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URL: https://oeis.org/A034960

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A034960
Divide odd numbers into groups with prime(n) elements and add together.
7
4, 21, 75, 189, 495, 897, 1683, 2565, 4071, 6641, 8959, 13209, 17835, 22317, 28623, 37577, 48439, 57401, 71623, 85697, 98623, 118737, 138195, 163493, 196231, 224321, 249775, 281945, 310759, 347249, 420751, 467801, 525943, 571985, 656047
OFFSET
1,1
LINKS
FORMULA
From Hieronymus Fischer, Sep 26 2012: (Start)
a(n) = Sum_{k=A007504(n-1)+1..A007504(n)} (2*k-1).
a(n) = A007504(n)^2 - A007504(n-1)^2.
a(n) = 2*A034957(n) + A000040(n).
a(n) = 2*A034956(n) - A000040(n).
a(n) = A034959(n) + A000040(n). (End)
a(n) = A061802(n)*A000040(n). - Marco Zárate, May 12 2023
EXAMPLE
{1,3} #2 S=4;
{5,7,9} #3 S=21;
{11,13,15,17,19} #5 S=75;
{21,23,25,27,29,31,33} #7 S=189.
MAPLE
S:= n-> sum(ithprime(k), k=1..n): seq(S(n+1)^2-S(n)^2, n=0..40); # Gary Detlefs, Dec 20 2011
MATHEMATICA
Accumulate[Join[{2}, ListConvolve[{1, 1}, #]]]*# & [Prime[Range[50]]] (* Paolo Xausa, Jun 23 2025 *)
PROG
(Python)
from itertools import islice
from sympy import nextprime
def A034960_gen(): # generator of terms
a, p = 0, 2
while True:
yield p*((a<<1)+p)
a, p = a+p, nextprime(p)
A034960_list = list(islice(A034960_gen(), 20)) # Chai Wah Wu, Mar 22 2023
(PARI) a0(n) = vecsum(primes(n))^2 - vecsum(primes(n-1))^2; \\ Michel Marcus, Jun 16 2024
KEYWORD
nonn
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved