The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A357251 a(n) = Sum_{1<=i<=j<=n} prime(i)*prime(j). 3
 4, 19, 69, 188, 496, 1029, 2015, 3478, 5778, 9519, 14479, 21768, 31526, 43609, 59025, 79218, 105178, 135739, 173795, 219164, 271140, 333629, 406171, 491878, 594698, 711959, 842151, 988848, 1150168, 1330177, 1548617, 1791098, 2063454, 2359107, 2698231, 3064708, 3470396, 3918157, 4404795, 4938846 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the sum of products of unordered pairs of (not necessarily distinct) elements from the first n primes. It appears that 4 is the only square in the sequence. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = (A007504(n)^2 + A024450(n))/2. a(n) = A024447(n) + A024450(n). a(n) = A065762(n)/2. - Hugo Pfoertner, Sep 24 2022 EXAMPLE a(3) = 2*2 + 2*3 + 2*5 + 3*3 + 3*5 + 5*5 = 69. MAPLE P:= [seq(ithprime(i), i=1..100)]: S:= ListTools:-PartialSums(P): ListTools:-PartialSums(zip(`*`, P, S)); MATHEMATICA Accumulate[(p = Prime[Range[40]]) * Accumulate[p]] (* Amiram Eldar, Sep 20 2022 *) PROG (Python) from itertools import accumulate from sympy import prime, primerange def aupton(nn): p = list(primerange(2, prime(nn)+1)) return list(accumulate(c*d for c, d in zip(p, accumulate(p)))) print(aupton(40)) # Michael S. Branicky, Sep 24 2022 after Amiram Eldar CROSSREFS Cf. A007504, A024447, A024450, A065762, A357252. Partial sums of A143215. Row n=2 of A343751. Sequence in context: A055485 A000306 A100185 * A291888 A217324 A129019 Adjacent sequences: A357248 A357249 A357250 * A357252 A357253 A357254 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Sep 20 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 18 21:51 EDT 2024. Contains 371781 sequences. (Running on oeis4.)