A323331 Smallest member of sociable quadruples using Dedekind psi function (A001615).

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

Author

Amiram Eldar, Jan 11 2019

Keywords

• nonn

Comments

Numbers k whose iterations of k -> A001615(k) - k are cyclic with a period of 4, and in each cyclic quadruple k is the least of the 4 members.

Examples

			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.
		

Crossrefs

Cf. A001615, A090615, A319902, A319915, A323327, A323328, A323329, A323330.

Programs

Mathematica

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