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A013940
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a(n) = Sum_{k=1..n} floor(n/prime(k)^2).
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6
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0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 14, 14, 14, 14, 15, 15, 15, 15, 16, 17, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 26, 26, 26, 26, 27, 27, 27, 27, 29
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OFFSET
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1,8
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1/(1 - x))*Sum_{k>=1} x^(prime(k)^2)/(1 - x^(prime(k)^2)). - Ilya Gutkovskiy, Feb 11 2017
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MAPLE
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A056170:= n -> nops(select(t -> (t[2]>1), ifactors(n)[2]));
N:= 10000; # to get terms up to a(N)
A:= map(round, Statistics:-CumulativeSum(Array(1..N, A056170)));
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MATHEMATICA
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Table[Sum[Floor[n/Prime[k]^2], {k, n}], {n, 70}] (* Harvey P. Dale, Mar 30 2018 *)
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PROG
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(PARI) a(n) = sum(k = 1, n, n\prime(k)^2); \\ Michel Marcus, Aug 24 2013
(PARI) a(n) = my(s=0); forprime(p=2, sqrtint(n), s += n\(p*p)); s; \\ Daniel Suteu, Nov 24 2018
(Magma) [(&+[Floor(n/NthPrime(k)^2): k in [1..n]]): n in [1..70]]; // G. C. Greubel, Nov 25 2018
(Sage) [sum(floor(n/nth_prime(k)^2) for k in (1..n)) for n in (1..70)] # G. C. Greubel, Nov 25 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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