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%I M1335 #44 Jul 25 2022 15:51:48
%S 2,5,7,12,13,23,19,31,30,45,33,67,43,65,65,84,61,107,69,123,97,115,85,
%T 175,110,147,133,179,111,223,129,215,175,203,179,302,159,235,215,315,
%U 181,337,193,315,285,287,213,451,246,371,299,393,243,461,301,461,343
%N Inverse Moebius transform of primes.
%C From _Davide Rotondo_, Mar 09 2022: (Start)
%C 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.
%C 2 3 5 7 11 13 17 19 23 29 ...
%C 0 2 0 3 0 5 0 7 0 11 ...
%C 0 0 2 0 0 3 0 0 5 0 ...
%C 0 0 0 2 0 0 0 3 0 0 ...
%C 0 0 0 0 2 0 0 0 0 3 ...
%C 0 0 0 0 0 2 0 0 0 0 ...
%C 0 0 0 0 0 0 2 0 0 0 ...
%C 0 0 0 0 0 0 0 2 0 0 ...
%C 0 0 0 0 0 0 0 0 2 0 ...
%C 0 0 0 0 0 0 0 0 0 2 ...
%C ...
%C ----------------------------------
%C Tot. 2 5 7 12 13 23 19 31 30 45 ... (End)
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Enrique Pérez Herrero, <a href="/A007445/b007445.txt">Table of n, a(n) for n = 1..5000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) = Sum_{d|n} prime(d).
%F G.f.: Sum_{k>=1} prime(k)*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Jan 02 2017
%e 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.
%t a[n_] := DivisorSum[n, Prime]; Array[a, 60] (* _Jean-François Alcover_, Dec 01 2015 *)
%o (PARI) je=[]; for(n=1,150,je=concat(je,sumdiv(n,d, prime(d)))); j
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Jason Earls_, Jul 08 2001
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