A133784 Positive integers n such that the sum of all primes <= n divides n(n+1)/2.

4, 21, 24, 71

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 21 2008

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A007504, A000217, A051349.

Programs

Maple

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);

Mathematica

Select[Range[2,100],Divisible[(#(#+1))/2,Total[Prime[Range[ PrimePi[ #]]]]]&] (* Harvey P. Dale, May 31 2012 *)

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

Extensions

Edited by Max Alekseyev, Feb 13 2009