A057246 s=0; d is divisor of n [here d <= n/d]; if gcd(d,n/d)=1 or gcd(d,n/d)=d then s=s+d+(n/d); [if d=n/d then s=s+d]: The sequence contains composite n for which s = 2*n.

6, 28, 6966, 15066

Offset

1,1

Comments

s(n) is a vaguely unitary analog of A060866. - R. J. Mathar, Oct 24 2011

No more terms up to 10^9. - Michel Marcus, Feb 24 2016

Links

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

Example

a(2)=28, gcd(1,28)=gcd(4,28/4)=1, gcd(2,28/2)=2, 1+28+4+7+2+14=56. 56-28=28.

Mathematica

f[ n_Integer ] := (ds = Divisors[ n ]; sq = N[ Sqrt[ n ] ]; l = 1; While[ ds[[ l ] ] <= sq, l++ ]; l = l - 1; ds = Take[ ds, l ]; s = 1; k = 2; While[ k <= l, If[ GCD[ ds[[ k ] ], n/ds[[ k ] ] ] == 1 || GCD[ ds[[ k ] ], n/ds[[ k ] ] ] == ds[[ k ] ], s = s + ds[[ k ] ] + n/ds[[ k ] ] ]; k++ ]; If[ ds[[ -1 ] ] == n/ds[[ -1 ] ], s = s - d ]; s) Do[ If[ ! PrimeQ[ n ] && f[ n ] == n, Print[ n ] ], {n, 2, 33429000} ] (* Robert G. Wilson v, Nov 09 2000 *)

Prog

(PARI) is(n)=my(s, g); fordiv(n, d, if(d^2<n&&((g=gcd(d, n/d))==1||g==d), s+=d+n/d)); g=sqrtint(n); if(n==g^2, s+=g); s==n+n \\ Charles R Greathouse IV, Oct 23 2011

Crossrefs

Sequence in context: A166998 A038182 A095723 * A154895 A330163 A276493

Adjacent sequences: A057243 A057244 A057245 * A057247 A057248 A057249

Keyword

more,nonn

Author

Naohiro Nomoto, Sep 21 2000

Status

approved