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

1, 3, 7, 13, 23, 35, 51, 69, 91, 119, 149, 185, 225, 267, 313, 365, 423, 483, 549, 619, 691, 769, 851, 939, 1035, 1135, 1237, 1343, 1451, 1563, 1689, 1819, 1955, 2093, 2241, 2391, 2547, 2709, 2875, 3047, 3225, 3405, 3595, 3787, 3983, 4181, 4391, 4613, 4839

Offset

1,2

Comments

Also: a(n) = sum_{k=1..n} phi(prime(k)).

Partial sums of A006093. - Omar E. Pol, Oct 31 2013

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

Sum of all deficiencies of the first n primes. - Omar E. Pol, Feb 21 2014

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

R. J. Cano, Additional information

R. J. Cano, PARI/GP code: alternative sequencer

Formula

a(n)=sum_{k=1..n} (prime(k)-1)

a(n)=A007504(n)-n. - Juri-Stepan Gerasimov, Nov 23 2009

A027424(A000040(n)) < a(n). - Charles R Greathouse IV, Apr 07 2021

Maple

seq((sum(phi(ithprime(x)), k=1..n)), n=1..100);

Mathematica

f[n_]:=Plus@@Prime[Range[n]]-n; Table[f[n], {n, 1, 50}] (* Enrique Pérez Herrero, Jun 10 2012 *)

Prog

(Haskell)
a101301 n = a101301_list !! (n-1)
a101301_list = scanl1 (+) a006093_list
-- Reinhard Zumkeller, May 01 2013
(PARI) a(n)=my(s); forprime(p=2, prime(n), s+=p); s-n \\ Charles R Greathouse IV, Oct 31 2013
(PARI) \\ See links.

Crossrefs

Cf. A000010, A000040, A006093, A005867.

Sequence in context: A053607 A209407 A124129 * A103116 A303853 A075321

Adjacent sequences: A101298 A101299 A101300 * A101302 A101303 A101304

Keyword

nonn,changed

Author

Jorge Coveiro, Dec 22 2004

Extensions

Name simplified by Juri-Stepan Gerasimov, Nov 23 2009

Status

approved