# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a093863 Showing 1-1 of 1 %I A093863 #11 Mar 02 2019 04:26:10 %S A093863 1,2,3,4,5,6,8,9,10,12,16,17,18,20,24,34,36,40,48,68,72,80,136,144, %T A093863 256,257,272,514,768,1028,1280,2056,2304,2808,4112,4320,4352,20280, %U A093863 65536,65537,65792,88704,131074,196416,196608,262148,327680,524296,589824,998400 %N A093863 Unitary sigma-unitary phi super perfect numbers: USUP(USUP(n))= n/k for some integer k. %C A093863 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. %C A093863 k = 2 for 4320, 20280, 88704, 196416, 998400, ... - _Amiram Eldar_, Mar 01 2019 %p A093863 for n from 1 to 20000 do if n mod A109712(A109712(n)) = 0 then printf("%d,",n); end if; end do: %t A093863 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 *) %Y A093863 Cf. A092760, A109712. %K A093863 nonn %O A093863 1,2 %A A093863 _Yasutoshi Kohmoto_, May 11 2004 %E A093863 More terms from _Amiram Eldar_, Mar 01 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE