A093863 Unitary sigma-unitary phi super perfect numbers: USUP(USUP(n))= n/k for some integer k.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24, 34, 36, 40, 48, 68, 72, 80, 136, 144, 256, 257, 272, 514, 768, 1028, 1280, 2056, 2304, 2808, 4112, 4320, 4352, 20280, 65536, 65537, 65792, 88704, 131074, 196416, 196608, 262148, 327680, 524296, 589824, 998400

Offset

1,2

Comments

USUP(.)= A109712(.). Where k values are 1, they define fixed points of the function USUP(USUP(n)). k values larger than 1 exist, for example USUP(USUP(4320))= 4320/2.

k = 2 for 4320, 20280, 88704, 196416, 998400, ... - Amiram Eldar, Mar 01 2019

Links

Table of n, a(n) for n=1..50.

Maple

for n from 1 to 20000 do if n mod A109712(A109712(n)) = 0 then printf("%d, ", n); end if; end do:

Mathematica

usigma[1]=1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); A047994[n_] := Times @@ (Power @@@ FactorInteger[n] - 1); A006519[n_] := 2^IntegerExponent[ n, 2]; usup[1] = 1; usup[n_ /; IntegerQ[Log[2, n]]] := n+1; usup[n_] := usigma[ A006519[n] ]*A047994[ n/A006519[n] ];  aQ[n_]:=Divisible[n, usup[usup[n]]]; Select[Range[10000], aQ] (* Amiram Eldar, Mar 01 2019 after Jean-François Alcover at A109712 *)

Crossrefs

Cf. A092760, A109712.

Sequence in context: A364541 A048645 A173786 * A337800 A091902 A067698

Adjacent sequences: A093860 A093861 A093862 * A093864 A093865 A093866

Keyword

nonn

Author

Yasutoshi Kohmoto, May 11 2004

Extensions

More terms from Amiram Eldar, Mar 01 2019

Status

approved