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A133784
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Positive integers n such that the sum of all primes <= n divides n(n+1)/2.
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2
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OFFSET
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1,1
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COMMENTS
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Also, positive integers n for which the sum of all primes <= n divides the sum of all nonprimes <= n.
Is this sequence finite?
No other terms below 10^13. - Max Alekseyev, Nov 28 2017
Sequence is probably complete; integral_{x=10^10..infinity} (2 log x)/x^2 dx = 4.80517... * 10^-9. - Charles R Greathouse IV, Mar 21 2013
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LINKS
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Table of n, a(n) for n=1..4.
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EXAMPLE
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n=21 is in this sequence since the sum of the primes <=21 is 2+3+5+7+11+13+17+19=77 and 77 divides 21*22/2=231.
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MAPLE
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P:=proc(n) local i, snp, sp; snp:=1; sp:=2; for i from 3 by 1 to n do if isprime(i) then sp:=sp+i; else snp:=snp+i; fi; if trunc(snp/sp)=snp/sp then print(i); fi; od; end: P(10000000);
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MATHEMATICA
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Select[Range[2, 100], Divisible[(#(#+1))/2, Total[Prime[Range[ PrimePi[ #]]]]]&] (* Harvey P. Dale, May 31 2012 *)
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PROG
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(PARI) A=1; P=0; for(n=2, 1e9, A+=n; P+=isprime(n)*n; if(A%P==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 21 2013
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CROSSREFS
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Cf. A007504, A000217, A051349.
Sequence in context: A303722 A305225 A272954 * A041821 A042429 A356357
Adjacent sequences: A133781 A133782 A133783 * A133785 A133786 A133787
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KEYWORD
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nonn
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AUTHOR
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Paolo P. Lava and Giorgio Balzarotti, Jan 21 2008
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EXTENSIONS
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Edited by Max Alekseyev, Feb 13 2009
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STATUS
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approved
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