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.
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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).
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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]
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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; }
Showing 1-2 of 2 results.
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