OFFSET
1,1
COMMENTS
From Davide Rotondo, Mar 09 2022: (Start)
Can be constructed by writing the sequence of prime numbers, then the sequence of prime numbers spaced by a zero, then the sequence of prime numbers spaced by two zeros, and so on. Finally add the values of the columns.
2 3 5 7 11 13 17 19 23 29 ...
0 2 0 3 0 5 0 7 0 11 ...
0 0 2 0 0 3 0 0 5 0 ...
0 0 0 2 0 0 0 3 0 0 ...
0 0 0 0 2 0 0 0 0 3 ...
0 0 0 0 0 2 0 0 0 0 ...
0 0 0 0 0 0 2 0 0 0 ...
0 0 0 0 0 0 0 2 0 0 ...
0 0 0 0 0 0 0 0 2 0 ...
0 0 0 0 0 0 0 0 0 2 ...
...
----------------------------------
Tot. 2 5 7 12 13 23 19 31 30 45 ... (End)
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{d|n} prime(d).
G.f.: Sum_{k>=1} prime(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Jan 02 2017
EXAMPLE
a(6)=23 because the divisors of 6 are: 1, 2, 3 and 6; and prime(1) + prime(2) + prime(3) + prime(6) = 2 + 3 + 5 + 13 = 23.
MATHEMATICA
a[n_] := DivisorSum[n, Prime]; Array[a, 60] (* Jean-François Alcover, Dec 01 2015 *)
PROG
(PARI) je=[]; for(n=1, 150, je=concat(je, sumdiv(n, d, prime(d)))); j
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Jason Earls, Jul 08 2001
STATUS
approved