1,1

Next term >300000. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2006

In base 12 the sequence becomes 6, 20, 24, 80, X6, 168, 280, 354, X80, 1054, 3680, 4854, 8368, 9228, 12280, 48X80, 56454, where X is 10 and E is 11. The perfect numbers (A000396 ) in this sequence in base 12 are are 6, 24, 354, 4854. - Walter Kehowski (wkehowski(AT)cox.net), May 20 2006

Jean-Marie De Koninck and Aleksandar Ivic, On a sum of divisors problem.

S={1}. Assume n>1 and that all numbers m<n have already been tested. Let s=sum{d: d|n, d<n, and d in S}. If s<=n, then n is now in S. The paper linked to above has some characterization results. - Walter Kehowski (wkehowski(AT)cox.net), May 20 2006

2 is in S since s=sum{d: d|n, d<n, and d in S} = sum{1} = 1 and 1<=2. Similarly, 3, 4, 5, 6 are in S with 6 as the first element such that s=n, that is, 6 is the first S-perfect number. - Walter Kehowski (wkehowski(AT)cox.net), May 20 2006

with(numtheory); S:={1}: SP:=[]: for w to 1 do for n from 1 to 2*10^5 do d:=select(proc(z) z in S and z<n end, divisors(n)); s:=convert(d, `+`); if s<=n then S:=S union {n} fi; if s=n then SP:=[op(SP), n]; print(n); fi; od; od; SP; - Walter Kehowski (wkehowski(AT)cox.net), May 20 2006

(C) #include <stdlib.h> #include <stdio.h> #define MAX_SIZE_SPERFSET 40 #define MAX_SIZE_SSET 300000 int main(int argc, char*argv[]) { int Sset[MAX_SIZE_SSET] ; int Ssetsize= 1; int Sperfset[MAX_SIZE_SPERFSET] ; int Sperfsetsize= 0; Sset[0]=1 ; for(int n=2; n < MAX_SIZE_SSET; n++) { int dsum=0 ; for(int i=0; i< Ssetsize; i++) { if( n % Sset[i] ==0 && Sset[i] < n) dsum += Sset[i] ; if (dsum > n || Sset[i] >=n) break ; } if( dsum <= n) { if(dsum==n) { Sperfset[Sperfsetsize++ ]=n ; printf("%d", n) ; } Sset[Ssetsize++ ]= n ; } } } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2006

Cf. A000396.

Sequence in context: A140347 A072710 A069235 this_sequence A064510 A114274 A110926

Adjacent sequences: A118369 A118370 A118371 this_sequence A118373 A118374 A118375

more,nonn

Vladeta Jovovic (vladeta(AT)Eunet.yu), May 15 2006

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2006