A319915 Smallest member of bi-unitary sociable quadruples.
162, 1026, 1620, 10098, 10260, 41800, 51282, 100980, 107920, 512820, 1479006, 4612720, 4938136, 14790060, 14800240, 23168840, 28158165, 32440716, 55204500, 81128632, 84392560, 88886448, 209524210, 283604220, 325903500, 498215416, 572062304, 881697520
Offset: 1
Keywords
Examples
162 is in the sequence since the iterations of the sum of bi-unitary proper divisors function (A188999(n) - n) are cyclic with a period of 4: 162, 174, 186, 198, 162, ... and 162 is the smallest member of the quadruple.
Programs
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Mathematica
fun[p_, e_]:=If[Mod[e, 2]==1, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bs[n_] := If[n==1, 1, Times @@ (fun @@@ FactorInteger[n])]-n;seq[n_]:=NestList [bs, n,4][[2;;5]] ;aQ[n_] := Module[ {s=seq[n]}, n==Min[s] && Count[s,n]==1]; Do[If[aQ[n],Print[n]],{n,1,10^9}] -
PARI
fn(n) = {if (n==1, 1, f = factor(n); for (i=1, #f~, p = f[i, 1]; e = f[i, 2]; f[i, 1] = if (e % 2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)); f[i, 2] = 1; ); factorback(f) - n;);} isok(n) = my(v = vector(5)); v[1] = n; for(k=2, 5, v[k] = fn(v[k-1])); (v[5] == n) && (vecmin(v) == n) && (#vecsort(v,,8)==4); \\ Michel Marcus, Oct 02 2018 -
PARI
is(n) = my(c = n); for(i = 1, 3, c = fn(c); if(c <= n, return(0))); c = fn(c); c == n \\ uses Michel Marcus' fn David A. Corneth, Oct 02 2018
Comments