A073033
A 4-cycle of the k => sigma(k)-k process, where sigma(k) is the sum of divisors of k (A000203).
Original entry on oeis.org
18656380, 20522060, 28630036, 24289964, 18656380, 20522060, 28630036, 24289964, 18656380, 20522060, 28630036, 24289964, 18656380, 20522060, 28630036, 24289964, 18656380, 20522060, 28630036, 24289964, 18656380, 20522060, 28630036, 24289964
Offset: 1
A119478
Smallest member of sociable sextuples.
Original entry on oeis.org
21548919483, 90632826380, 1771417411016, 3524434872392, 4773123705616
Offset: 1
- David Moews and Paul C. Moews, A search for aliquot cycles and amicable pairs, Mathematics of computation, Vol. 61, No. 204 (1993), pp. 935-938.
- David Moews, A list of currently known aliquot cycles of length greater than 2.
- Jan Munch Pedersen, Known Sociable Numbers of order different from four, Tables of Aliquot Cycles.
- Jan Munch Pedersen, Sociable number of order 6, Tables of Aliquot Cycles.
- Eric Weisstein's World of Mathematics, Sociable Numbers.
- Wikipedia, Sociable number.
A214134
Smallest member of sociable quadruples that follow W. Borho's construction rule.
Original entry on oeis.org
28158165, 2387776550, 88585861815, 111375706442, 1092162882824, 39436853599990, 65747483238255, 92180272746590, 96642590616495, 209709847893070, 223599822374385, 430324482433184, 535975018716375, 1107681705347175, 1210691484867410, 1356505589071269
Offset: 1
b-file removed and construction rules updated by
Michel Marcus, Dec 04 2014
A323331
Smallest member of sociable quadruples using Dedekind psi function (A001615).
Original entry on oeis.org
11398670, 22797340, 38369450, 45594680, 56993350, 59334310, 76738900, 91189360, 113986700, 118668620, 153477800, 182378720, 209524210, 227973400, 237337240, 268586150, 284966750, 306955600, 364757440, 419048420, 455946800, 474674480, 537172300, 539867650, 569933500
Offset: 1
11398670 is in the sequence since the iterations of k -> A001615(k) - k are cyclic with a period of 4: 11398670, 11475730, 12474350, 14093650, 11398670, ... and 11398670 is the smallest member of the quadruple.
-
t[0]=0; t[1]=0; t[n_]:=(Times@@(1+1/Transpose[FactorInteger[n]][[1]])-1)*n;
seq[n_]:=NestList [t, n, 4][[2;; 5]] ; aQ[n_] := Module[ {s=seq[n]}, n==Min[s] && Count[s, n]==1]; s={}; Do[If[aQ[n], AppendTo[s, n]], {n, 1, 10^9}]; s
A361811
Smallest members of infinitary sociable quadruples.
Original entry on oeis.org
1026, 10098, 10260, 41800, 45696, 100980, 241824, 685440, 4938136, 13959680, 14958944, 25581600, 28158165, 32440716, 36072320, 55204500, 74062944, 81128632, 149589440, 178327008, 192793770, 209524210, 283604220, 319848642, 498215416, 581112000, 740629440, 1236402232
Offset: 1
1026 is a term since the iterations of the sum of aliquot infinitary divisors function (A126168) that start with 1026 are cyclic with period 4: 1026, 1374, 1386, 1494, 1026, ..., and 1026 is the smallest member of the quadruple.
The first five quadruples are {1026, 1374, 1386, 1494}, {10098, 15822, 19458, 15102}, {10260, 13740, 13860, 14940}, {41800, 51800, 66760, 83540}, {45696, 101184, 94656, 88944}.
Subsequence of
A004607 (all cycles of length > 2).
-
f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]]>0, 1 + p^(2^(m-j)), 1], {j, 1, m}]]; infs[n_] := Times @@ f @@@ FactorInteger[n] - n; infs[1] = 0; seq[n_] := NestList[infs, n, 4][[2;; 5]] ; q[n_] := Module[{s = seq[n]}, n == Min[s] && Count[s, n] == 1]; Select[Range[10^6], q]
-
infs(n) = {my(f = factor(n), b); prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], f[i, 1]^(2^(#b-k)) + 1, 1))) - n; }
is(n) = {my(m = n); for(k = 1, 4, m = infs(m); if(k < 4 && m <= n, return(0))); m == n; }
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