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

1,1

Comments

The bi-unitary version of A090615.

Links

Table of n, a(n) for n=1..28.

Example

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.

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}]

Prog

(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

Crossrefs

Cf. A090615, A188999, A292980, A292981, A319902.

Sequence in context: A044985 A302283 A186844 * A302731 A206145 A342850

Adjacent sequences: A319912 A319913 A319914 * A319916 A319917 A319918

Keyword

nonn

Author

Amiram Eldar, Oct 01 2018

Status

approved