A196421 a(n) = prime(n)*T(n), where T = A000217.

2, 9, 30, 70, 165, 273, 476, 684, 1035, 1595, 2046, 2886, 3731, 4515, 5640, 7208, 9027, 10431, 12730, 14910, 16863, 19987, 22908, 26700, 31525, 35451, 38934, 43442, 47415, 52545, 62992, 69168, 76857, 82705, 93870, 100566, 110371, 120783, 130260, 141860

Offset

1,1

Comments

This sequence is mentioned in A077320. - Omar E. Pol, Mar 12 2012

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ 0.5 n^3 log n. - Charles R Greathouse IV, Nov 22 2011

a(n) = A000040(n)*A000217(n). - Omar E. Pol, Mar 12 2012

Example

The 4th prime is 7, the 4th triangular number is 10, therefore a(4) = 7*10 = 70.

Mathematica

With[{nn=60}, Prime[Range[nn]]Accumulate[Range[nn]]]

Prog

(PARI) a(n)=prime(n)*binomial(n+1, 2) \\ Charles R Greathouse IV, Nov 22 2011
(Python)
from sympy import prime
def a(n): return prime(n) * n*(n+1)//2
print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Sep 01 2022

Crossrefs

Cf. A000040, A000217.

Row sums of triangle A077320. - Omar E. Pol, Mar 12 2012

Subsequence of A085783. - Michel Marcus, May 15 2018

Sequence in context: A079783 A182975 A228932 * A352405 A372152 A056778

Adjacent sequences: A196418 A196419 A196420 * A196422 A196423 A196424

Keyword

nonn

Author

Harvey P. Dale, Oct 15 2011

Status

approved