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 A118372 S-perfect numbers. 8
 6, 24, 28, 96, 126, 224, 384, 496, 1536, 1792, 6144, 8128, 14336, 15872, 24576, 98304, 114688, 393216, 507904, 917504, 1040384, 1572864, 5540590, 6291456, 7340032, 9078520, 16252928, 22528935, 25165824, 33550336, 56918394, 58720256, 100663296, 133169152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 6, 24, 354, 4854. - Walter Kehowski, May 20 2006 Subsequence of A083207. - Reinhard Zumkeller, Oct 28 2010 Conjecture: If k is an S-perfect number, then A000203(k)/2 is a Zumkeller number (A083207). - Ivan N. Ianakiev, Apr 23 2017 LINKS Donovan Johnson, Table of n, a(n) for n = 1..40 (terms < 4*10^9) Jean-Marie De Koninck and Aleksandar Ivic, On a sum of divisors problem, Publications de l'Institut Mathématique (Beograd), New Series, Vol. 64(78), pp. 9--20 (1998) FORMULA S={1}. Assume n>1 and that all numbers m n, and S_{n-1} U {n} if s_n <= n. - Hugo van der Sanden, Oct 28 2010 EXAMPLE 2 is in S since s=sum{d: d|n, d #include #define MAX_SIZE_SSET 1000000 int main(int argc, char*argv[]) { int Sset[MAX_SIZE_SSET] ; int Ssetsize= 1; Sset=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) printf("%d\n", n) ; Sset[Ssetsize++ ]= n ; } } } /* R. J. Mathar, Oct 28 2010 */ (Haskell) a118372_list = sPerfect 1 [] where    sPerfect x ss | v > x = sPerfect (x + 1) ss                  | v < x = sPerfect (x + 1) (x : ss)                  | otherwise = x : sPerfect (x + 1) (x : ss)                  where v = sum (filter ((== 0) . mod x) ss) -- Reinhard Zumkeller, Feb 25 2012, Oct 28 2010 (Sage) def S_perfect_list(search_limit):     S = []; T = []     for n in (1..search_limit):         d = [t for t in divisors(n) if t in S and t < n]         s = sum(d)         if s <= n: S.append(n)         if s == n: T.append(n)     return T S_perfect_list(25555) # after Walter Kehowski, Peter Luschny, Sep 03 2018 CROSSREFS Subsequence of A023196; A000396 is a subsequence. Cf. A181487. Sequence in context: A293453 A336641 A336550 * A263928 A219362 A226476 Adjacent sequences:  A118369 A118370 A118371 * A118373 A118374 A118375 KEYWORD nonn AUTHOR Vladeta Jovovic, May 15 2006 EXTENSIONS More terms from R. J. Mathar, May 17 2006, a(18) and a(19) Oct 28 2010 Two more terms added and C-program reduced by R. J. Mathar, Oct 28 2010 More terms from William Rex Marshall, Oct 28 2010 Haskell program improved by Reinhard Zumkeller, Nov 02 2010 STATUS approved

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Last modified January 20 12:40 EST 2021. Contains 340302 sequences. (Running on oeis4.)