A163636 The sum of all odd numbers from 2n-1 up to the n-th odd nonprime.

1, 24, 60, 112, 153, 171, 253, 275, 336, 448, 525, 555, 640, 672, 828, 864, 969, 1155, 1197, 1320, 1449, 1495, 1632, 1680, 1728, 1875, 2133, 2407, 2580, 2640, 2700, 2760, 2820, 2880, 3069, 3264, 3328, 3672, 3740, 3808, 3876, 4248, 4320, 4551, 4625, 4864

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A005408(n-1)+A005408(n)+...+A014076(n);

a(n) = ( A014076(n)+2*n-1 ) *( A014076(n)-2*n+3 )/4.

Example

a(1)=1. a(2)=3+5+7+9=24. a(3)=5+7+9+11+13+15=60.

Maple

A014076 := proc(n) option remember; local a; if n = 1 then 1; else for a from procname(n-1)+2 by 2 do if not isprime(a) then RETURN(a) ; fi; od: fi; end:
A163636 := proc(n) local onpr; onpr := A014076(n) ; (onpr+2*n-1)*(onpr-2*n+3)/4; end: seq(A163636(n), n=1..80) ; # R. J. Mathar, Aug 08 2009

Mathematica

A014076 := Select[Range[1, 10299, 2], PrimeOmega[#] != 1 &]; Table[(A014076[[n]] + 2*n - 1)*(A014076[[n]] - 2*n + 3)/4, {n, 1, 50}] (* G. C. Greubel, Jul 31 2017 *)
Module[{nn=201, onp}, onp=Select[Range[1, nn, 2], !PrimeQ[#]&]; Table[Total[ Range[ 2n-1, onp[[n]], 2]], {n, Length[onp]}]] (* Harvey P. Dale, Jul 03 2020 *)

Prog

(Python)
from sympy import primepi
def A163636(n):
    if n == 1: return 1
    m, k, n2 = n-1, primepi(n) + n - 1 + (n>>1), (n<<1)-1
    while m != k:
        m, k = k, primepi(k) + n - 1 + (k>>1)
    return (lambda x: (x+n2)*(x-n2+2)>>2)(m) # Chai Wah Wu, Jul 31 2024

Crossrefs

Cf. A005408, A014076.

Sequence in context: A044126 A044507 A101860 * A279930 A292891 A366751

Adjacent sequences: A163633 A163634 A163635 * A163637 A163638 A163639

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Aug 02 2009

Extensions

Edited and a(21) corrected by R. J. Mathar, Aug 08 2009

Status

approved