A051152 - OEIS

A051152

(-1)sigma sociable number of order 2: (-1)sigma((-1)sigma(x))=x, but (-1)sigma(x)<>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 #18 Jul 14 2024 20:49:42

%S 4,5,216,494,16800,21228,246400,440220

%N (-1)sigma sociable number of order 2: (-1)sigma((-1)sigma(x))=x, but (-1)sigma(x)<>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 Factorizations: 4, 5, 2^3*3^3, 2*13*19, 2^5*3*5^2*7, 2^2*3*29*61

%o (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) ; }

%o isA051152(r)={ local(s,t) ; s=A049060(r) ; t=A049060(s) ; if( r == t && s !=r, return(1), return(0) ) ; }

%o { for(n=1,30000000, if( isA051152(n), print(n," ") ) ; ) ; } \\ _R. J. Mathar_, Oct 12 2006

%Y Cf. A049057, A049058, A049059, A049060, A034094, A051153.

%K nonn,more

%O 0,1

%A _Yasutoshi Kohmoto_

%E More terms from _R. J. Mathar_, Oct 12 2006