

A274140


Sum of primes dividing nth 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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..79.
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/((1x)^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[1]=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)[1], 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



