cp's OEIS Frontend

A101301 The sum of the first n primes, minus n.

%I A101301 #42 Dec 19 2024 11:46:19
%S A101301 1,3,7,13,23,35,51,69,91,119,149,185,225,267,313,365,423,483,549,619,
%T A101301 691,769,851,939,1035,1135,1237,1343,1451,1563,1689,1819,1955,2093,
%U A101301 2241,2391,2547,2709,2875,3047,3225,3405,3595,3787,3983,4181,4391,4613,4839
%N A101301 The sum of the first n primes, minus n.
%C A101301 Also: a(n) = sum_{k=1..n} phi(prime(k)).
%C A101301 Partial sums of A006093. - _Omar E. Pol_, Oct 31 2013
%C A101301 Difference minus n, between the constant term prime(n) for a polynomial P(x) built from the first n primes took as coefficients and the value that such term should have in order to make P(x) divisible by (x-1). See links. - _R. J. Cano_, Jan 14 2014
%C A101301 Sum of all deficiencies of the first n primes. - _Omar E. Pol_, Feb 21 2014
%H A101301 Enrique Pérez Herrero, <a href="/A101301/b101301.txt">Table of n, a(n) for n = 1..5000</a>
%H A101301 R. J. Cano, <a href="http://oeis.org/w/images/2/26/DaysYearsPermute.pdf">Additional information</a>
%H A101301 R. J. Cano, <a href="http://oeis.org/w/images/9/98/A101301.gp.txt">PARI/GP code: alternative sequencer</a>
%F A101301 a(n)=sum_{k=1..n} (prime(k)-1)
%F A101301 a(n)=A007504(n)-n. - _Juri-Stepan Gerasimov_, Nov 23 2009
%F A101301 A027424(A000040(n)) < a(n). - _Charles R Greathouse IV_, Apr 07 2021
%p A101301 seq((sum(phi(ithprime(x)),k=1..n)),n=1..100);
%t A101301 f[n_]:=Plus@@Prime[Range[n]]-n; Table[f[n],{n,1,50}] (* _Enrique Pérez Herrero_, Jun 10 2012 *)
%o A101301 (Haskell)
%o A101301 a101301 n = a101301_list !! (n-1)
%o A101301 a101301_list = scanl1 (+) a006093_list
%o A101301 -- _Reinhard Zumkeller_, May 01 2013
%o A101301 (PARI) a(n)=my(s);forprime(p=2,prime(n),s+=p); s-n \\ _Charles R Greathouse IV_, Oct 31 2013
%o A101301 (PARI) \\ See links.
%Y A101301 Cf. A000010, A000040, A006093, A005867.
%K A101301 nonn
%O A101301 1,2
%A A101301 _Jorge Coveiro_, Dec 22 2004
%E A101301 Name simplified by _Juri-Stepan Gerasimov_, Nov 23 2009