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A134125 Integral quotients of partial sums of primes divided by the number of summations. 5
5, 5, 7, 11, 16, 107, 338, 1011, 2249, 22582, 35989, 39167, 61019, 186504, 248776, 367842, 977511, 1790714, 7104697, 15450640, 42428590, 81262621, 232483021, 319278215, 364554172, 419271517, 4432367717, 14591939203, 46911464601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With 1 summation, the partial sum is 2+3=5 and 5/1=5 is integer, added to sequence. With 2 summations, the partial sum is 2+3+5=10 and 10/2=5 is integer, added to the sequence. After 3 summations, 2+3+5+7=17 and 17/3=5.6.. is not integer, no contribution to the sequence.

These are all integers of the form A007504(k+1)/k, occurring at k in A134126. Similar to A050248, which looks at A007504(k)/k. - R. J. Mathar, Oct 23 2007

LINKS

Table of n, a(n) for n=1..29.

FORMULA

a(n) = A007504(k+1)/k where k = A134126(n).

EXAMPLE

a(1)=5 because 2+3=5 and 5/1=5, an integral quotient. a(3)= A007504(5)/4 = 28/4 =7. a(4)=A007504(8)/7 = 77/7 =11.

MATHEMATICA

With[{nn=50000000}, Select[Rest[Accumulate[Prime[Range[nn]]]]/Range[nn-1], IntegerQ]] (* Harvey P. Dale, Jul 25 2013 *)

PROG

UBASIC: 10 'primes using counters 20 N=3:C=1:R=5:print 2; 3, 5 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then N=N+2:goto 30 60 A=A+2:O=A 70 if A<=sqrt(N) then 40 80 C=C+1 90 R=R+N:T=R/C:U=R-N 100 if T=int(T) then print C; U; N; R; T:stop 110 N=N+2:goto 30

CROSSREFS

Cf. A134126, A134127, A134128, A134129.

Sequence in context: A196351 A154583 A300916 * A097996 A033300 A134130

Adjacent sequences:  A134122 A134123 A134124 * A134126 A134127 A134128

KEYWORD

nonn

AUTHOR

Enoch Haga, Oct 09 2007

EXTENSIONS

a(21) from R. J. Mathar, Oct 23 2007

Edited by R. J. Mathar, Apr 17 2009

a(22)-a(29) from Max Alekseyev, Jan 28 2012

STATUS

approved

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Last modified September 20 10:10 EDT 2019. Contains 327229 sequences. (Running on oeis4.)