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A101301 The sum of the first n primes, minus n. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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 A075321 A258030

Adjacent sequences:  A101298 A101299 A101300 * A101302 A101303 A101304

KEYWORD

nonn

AUTHOR

Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 22 2004

EXTENSIONS

Name simplified by Juri-Stepan Gerasimov, Nov 23 2009

STATUS

approved

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Last modified July 27 04:25 EDT 2017. Contains 289841 sequences.