cp's OEIS Frontend

A051153 (-1)-sigma super perfect numbers: (-1)sigma((-1)sigma(x))=2*x, where if x=Product p(i)^r(i) then (-1)sigma(x)=Product (-1+Sum p(i)^s(i), s(i)=1 to r(i)); (-1)sigma(1)=1.

%I A051153 #14 Jul 14 2024 15:35:40
%S A051153 247,988,2808,10440,87696,151200,191052,263520,2630320,3961980
%N A051153 (-1)-sigma super perfect numbers: (-1)sigma((-1)sigma(x))=2*x, where if x=Product p(i)^r(i) then (-1)sigma(x)=Product (-1+Sum p(i)^s(i), s(i)=1 to r(i)); (-1)sigma(1)=1.
%C A051153 Factorizations: 13*19, 2^3*3^2*5*29, 2^4*3^3*7*29, 2^5*3^3*5^2*7, 2^2*3^3*29*61, 2^5*3^3*5*61, 2^7*3*5*11*19*29*1021
%F A051153 A049060(A049060(n))=2n. - _R. J. Mathar_, Oct 12 2006
%o A051153 (PARI) A049060(n)={ local(i,resul,rmax,p) ; if(n==1, return(1) ) ; i=factor(n) ; rmax=matsize(i)[1] ; resul=1 ; for(r=1,rmax, p=0 ; for(j=1,i[r,2], p += i[r,1]^j ; ) ; resul *= p-1 ; ) ; return(resul) ; } isA051153(r)={ local(s,t) ; s=A049060(r) ; t=A049060(s) ; if( 2*r == t, return(1), return(0) ) ; } { for(n=1,30000000, if( isA051153(n), print(n,",") ) ; ) ; } \\ _R. J. Mathar_, Oct 12 2006
%Y A051153 Cf. A049057, A049058, A049059, A049060, A034094, A051152.
%K A051153 nonn,more
%O A051153 1,1
%A A051153 _Yasutoshi Kohmoto_
%E A051153 Corrected and extended by _R. J. Mathar_, Oct 12 2006