A034960 - OEIS

A034960

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

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

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

CROSSREFS

Cf. A006003, A027441, A034959.

Cf. A007504.

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

Sequence in context: A095668 A078800 A184706 * A240372 A157493 A192429

Adjacent sequences: A034957 A034958 A034959 * A034961 A034962 A034963

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 15 1998

STATUS

approved