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A007445 Inverse Moebius transform of primes.

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