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A133447 Nonsemiprime hyperperfect numbers.

%I A133447 #26 Mar 24 2025 06:04:33
%S A133447 325,2133,10693,16513,19521,51301,159841,176661,214273,306181,1433701,
%T A133447 1570153,1950625,2469601,2924101,5199013,9398593,10445221,15407173,
%U A133447 23548753,28600321,39147301,60110701,62722153,88347781,112803841
%N A133447 Nonsemiprime hyperperfect numbers.
%C A133447 The other 25 of the first 35 values of A007592 are all semiprimes A001358.
%C A133447 This sequence excludes perfect numbers (A000396), which are 1-hyperperfect numbers. - _Jud McCranie_, Mar 23 2025.
%H A133447 Jud McCranie, <a href="/A133447/b133447.txt">Table of n, a(n) for n = 1..1167 (terms < 10^15)</a>.  Earlier terms from Jonathan Vos Post and R. J. Mathar, and a b-file with 192 terms (to 10^12) by Donovan Johnson.
%F A133447 A100959 INTERSECTION A007592.
%e A133447 a(1) = 325 = 5^2 * 13.
%e A133447 a(2) = 2133 = 3^3 * 79.
%e A133447 a(3) = 10693 = 17^2 * 37.
%e A133447 a(4) = 16513 = 7^2 * 337.
%e A133447 a(5) = 19521 = 3^4 * 341.
%e A133447 a(6) = 51301 = 29^2 * 61.
%e A133447 a(7) = 159841 = 11^2 * 1321.
%e A133447 a(8) = 176661 = 3^5 * 727.
%e A133447 a(9) = 214273 = 47^2 * 97.
%e A133447 a(10) = 306181 = 53^2 * 109.
%e A133447 a(12) = 1570153 = 13 * 269 * 449. - _Jud McCranie_, Mar 23 2025
%p A133447 a034897 := [] : fd := fopen("b034897.txt",READ) : bf := fscanf(fd,"%d %d") : while nops(bf) <> 0 do a034897 := [op(a034897), op(2,bf) ] ; bf := fscanf(fd,"%d %d") ; od: a007592 := [] : for n in a034897 do m := (n-1)/( numtheory[sigma](n)-n-1) ; if m > 1 then a007592 := [op(a007592),n] ; fi ; od: isA100959 := proc(n) if numtheory[bigomega](n) <> 2 then true ; else false ; end: end: for n in a007592 do if isA100959(n) then printf("%d, ",n) ; fi ; od: # _R. J. Mathar_, Jan 08 2008
%Y A133447 Cf. A001358, A007592, A100959.
%K A133447 nonn
%O A133447 1,1
%A A133447 _Jonathan Vos Post_, Dec 22 2007
%E A133447 More terms from _R. J. Mathar_, Jan 08 2008