The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A274140 Sum of primes dividing n-th triangular number, counted with multiplicity. 0
 0, 3, 5, 7, 8, 10, 11, 10, 11, 16, 16, 18, 20, 15, 14, 23, 23, 25, 26, 17, 21, 34, 30, 17, 23, 22, 18, 38, 37, 39, 39, 22, 31, 29, 20, 45, 56, 35, 25, 50, 51, 53, 56, 24, 34, 70, 56, 23, 24, 30, 35, 68, 62, 25, 27, 33, 51, 88, 69, 71, 92, 44, 23, 28, 32, 81, 86, 45, 38, 83, 81, 83, 110, 50, 34, 39, 34, 95, 90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Eric Weisstein's World of Mathematics, Sum of prime factors Eric Weisstein's World of Mathematics, Triangular number FORMULA For any integer coefficient C(n) of the polynomial generated by the Triangular Numbers generating function f(x)=x/((1-x)^3), if C(n) = Product (p_j^k_j) then a(n) = Sum (p_j * k_j). a(n) = A001414(A000217(n)). EXAMPLE a(4) = 7; the 4th triangular number is 10, the prime factors of 10 are 2 and 5, and 2+5 = 7. a(6) = 10; the 6th triangular number is 21, the prime factors of 21 are 3 and 7, and 3+7 = 10. MATHEMATICA a=0; a[n_] := Plus @@ Times @@@ FactorInteger[n (n+1)/2]; Array[a, 80] (* Giovanni Resta, Jun 12 2016 *) PROG (PARI) a(n) = my(f=factor(n*(n+1)/2)); sum(i=1, matsize(f), f[i, 1]*f[i, 2]) \\ David A. Corneth, Jun 12 2016 CROSSREFS Cf. A000217 (triangular numbers), A001414 (sum of primes dividing n). Sequence in context: A175144 A183054 A188569 * A212294 A299495 A186689 Adjacent sequences:  A274137 A274138 A274139 * A274141 A274142 A274143 KEYWORD nonn AUTHOR Luca Pezzullo, Jun 11 2016 EXTENSIONS a(30) and a(38) corrected by Giovanni Resta, Jun 12 2016 STATUS approved

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

Last modified July 10 16:22 EDT 2020. Contains 335577 sequences. (Running on oeis4.)