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A093863
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Unitary sigma-unitary phi super perfect numbers: USUP(USUP(n))= n/k for some integer k.
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0
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=1..50.
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MAPLE
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for n from 1 to 20000 do if n mod A109712(A109712(n)) = 0 then printf("%d, ", n); end if; end do:
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A092760, A109712.
Sequence in context: A029509 A048645 A173786 * A337800 A091902 A067698
Adjacent sequences: A093860 A093861 A093862 * A093864 A093865 A093866
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto, May 11 2004
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EXTENSIONS
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More terms from Amiram Eldar, Mar 01 2019
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STATUS
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approved
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