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Numbers k such that A000217(k)/A006218(k) is an integer.
1

%I #29 Mar 04 2024 01:09:46

%S 1,2,47,347,348,6930,6947,6948,69269,379131,4011952,8280003

%N Numbers k such that A000217(k)/A006218(k) is an integer.

%C The next term, if it exists, is > 10^9. - _Vaclav Kotesovec_, Oct 16 2018

%C The next term, if it exists, is > 10^10. - _Charles R Greathouse IV_, Nov 05 2021

%o (PARI) is(n)=my(m=sum(k=1,sqrtint(n),n\k)*2-sqrtint(n)^2); n^2%m==0 \\ _Charles R Greathouse IV_, Nov 04 2021

%o (PARI) A006218(n)=sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2

%o list(lim,startAt=1)=startAt=ceil(startAt); my(v=List(), s=A006218(startAt-1)); for(n=startAt, lim, s+=numdiv(n); if(binomial(n+1,2)%s==0, listput(v,n))); Vec(v) \\ _Charles R Greathouse IV_, Nov 04 2021

%Y Cf. A000217, A006218, A000005.

%K more,nonn

%O 1,2

%A _Ctibor O. Zizka_, May 30 2009

%E a(9)-a(10) from _R. J. Mathar_, Aug 30 2010

%E a(11) from _Paolo P. Lava_, May 06 2015

%E a(12) from _Vaclav Kotesovec_, Oct 14 2018