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

4, 21, 24, 71

Offset

1,1

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

Links

Table of n, a(n) for n=1..4.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A007504, A000217, A051349.

Sequence in context: A303722 A305225 A272954 * A041821 A042429 A356357

Adjacent sequences: A133781 A133782 A133783 * A133785 A133786 A133787

Keyword

nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 21 2008

Extensions

Edited by Max Alekseyev, Feb 13 2009

Status

approved