

A101696


a(n) = sum(i=1,n)(ith ialmost prime). Cumulative sums of A101695.


2



2, 8, 26, 66, 174, 398, 878, 2174, 4862, 10494, 22014, 45054, 98302, 222718, 480766, 1021438, 2127358, 4355582, 8943102, 18773502, 38696446, 79590910, 175142398, 368080382, 764442110, 1586525694, 3247470078, 6644856318, 13489960446
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OFFSET

1,1


COMMENTS

It seems that this sum can never be a prime after a(1) = 2, since the nth nalmost prime is always even. The number of prime factors (with multiplicity) of a(n) is 1, 3, 2, 3, 3, 2, 2, 2, 4, 5, 4, 4, 3, 3, 5, 4, 3, 4, 7, 4, 2, 5, 5, 2, 3, 7, 4, 3, 4.
This is the diagonalization of the set of sequences {jalmost prime(k)}. The cumulative sums of this sequence are in A101696. a(1)=2 is prime. a(2)=8 is a 3almost prime. a(3)=26 is a semiprime. a(4)=66 is a 3almost prime. a(5)= 174 is a 3almost prime. a(6)=398 is a semiprime. a(7)=878 is a semiprime. a(8)=2174 is a semiprime. a(9)=4862 is a 4almost prime. a(10)=10494 is a 5almost prime. a(11)=22014 is a 4almost prime. a(12)=45054 is a 3almost prime. a(13)=98302 is a 3almost prime. a(14)=222718 is a 3almost prime. a(15)=480766 is a 5almost prime. a(16)=1021438 is a 4almost prime. a(17)=2127358 is a 3almost prime. a(18)=4355582 is a 4almost prime. a(19)=8943102 is a 7almost prime. a(20)=18773502 is a 4almost prime. 21almost numbers are not yet listed in the OEIS.


LINKS



FORMULA

a(1) = first 1almost prime = first prime = A000040(1). a(2) = a(1) + 2nd 2almost prime = a(1) + 2nd semiprime = A000040(1)+A001358(2). a(3) = a(2) + 3rd 3almost prime = a(2) + A014612(3). a(4) = a(3) + 4th 4almost prime = a(3) + A014613(4)... a(n) = a(n1) + nth nalmost prime.


EXAMPLE

a(1) = first 1almost prime = first prime = A000040(1) = 2.
a(2) = 2 + 2nd 2almost prime = 2 + A001358(2) = 2+ 6 = 8.
a(3) = a(2) + 3rd 3almost prime = 8+A014612(3) = 8+18 = 26.
a(4) = a(3) + 4th 4almost prime = 26+A014613(4) = 26+40 = 66.
a(5) = a(4) + 5th 5almost prime = 66+A014614(5) = 66+108=174.
...
a(12) = a(11) + 12th 12almost prime = 22014 + 23040 = 45054 (the first nontrivial palindrome in the sequence).


CROSSREFS

Cf. A000040, A001358, A014612, A014613, A046314, A046306, A046308, A046310, A046312, A046314, A069272, A069273, A069274, A069275, A069276, A069277, A069278, A069279, A069280, A069281, A101637, A101638, A101605, A101606, A101695.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



