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A308495 a(n) is the position of the first occurrence of prime(n) in A027748.

%I A308495 #36 Jan 11 2025 18:50:28
%S A308495 2,3,5,8,13,16,22,25,32,41,45,55,62,66,73,83,94,98,109,117,120,132,
%T A308495 138,150,166,173,177,185,188,196,224,231,243,247,267,271,284,295,303,
%U A308495 315,327,331,353,356,364,368,394,419,426,430,439,452,456,475,487,500
%N A308495 a(n) is the position of the first occurrence of prime(n) in A027748.
%H A308495 Alois P. Heinz, <a href="/A308495/b308495.txt">Table of n, a(n) for n = 1..10000</a>
%F A308495 A027748(a(n)) = A000040(n).
%F A308495 a(n) = 1 + A013939(A000040(n)). - _Charlie Neder_, Jun 04 2019
%F A308495 a(n) = A082186(A000040(n)). - _Alois P. Heinz_, Jun 06 2019
%F A308495 a(n) = 1 + Sum_{k=1..n} floor(prime(n)/prime(k)). - _Benoit Cloitre_, Jan 11 2025
%e A308495 For n = 5: a(5) = 13, A027748(13) = A000040(5) = 11.
%p A308495 b:= proc(n) option remember; `if`(n=1, 1,
%p A308495       b(n-1) +nops(ifactors(n)[2]))
%p A308495     end:
%p A308495 a:= n-> b(ithprime(n)):
%p A308495 seq(a(n), n=1..60);  # _Alois P. Heinz_, Jun 06 2019
%t A308495 b[n_] := b[n] = If[n == 1, 1, b[n-1] + PrimeNu[n]];
%t A308495 a[n_] := b[Prime[n]];
%t A308495 Array[a, 60] (* _Jean-François Alcover_, Nov 27 2020, after _Alois P. Heinz_ *)
%o A308495 (Haskell)
%o A308495 -- expected to be part of A027748
%o A308495 a027748_list = concat (map a027748_row [1..])
%o A308495 minIdx [] _ = []
%o A308495 minIdx _ [] = []
%o A308495 minIdx (a:as) (b:bs)
%o A308495     | a == b = 1 : (map succ (minIdx as bs))
%o A308495     | otherwise = map succ (minIdx as (b:bs))
%o A308495 a308495_list = minIdx a027748_list a000040_list
%o A308495 a308495 n = a308495_list !! (n-1)
%o A308495 (PARI) a(n) = 1 + sum(k=1, prime(n), omega(k)); \\ _Michel Marcus_, Jun 05 2019
%Y A308495 Cf. A000040, A001221, A013939, A027748, A082186.
%K A308495 nonn
%O A308495 1,1
%A A308495 _Peter Dolland_, Jun 01 2019