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.

247, 988, 2808, 10440, 87696, 151200, 191052, 263520, 2630320, 3961980

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..10.

Formula

A049060(A049060(n))=2n. - R. J. Mathar, Oct 12 2006

Prog

(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

Crossrefs

Cf. A049057, A049058, A049059, A049060, A034094, A051152.

Sequence in context: A063356 A250608 A127349 * A166399 A129133 A251265

Adjacent sequences: A051150 A051151 A051152 * A051154 A051155 A051156

Keyword

nonn

Author

Yasutoshi Kohmoto

Extensions

Corrected and extended by R. J. Mathar, Oct 12 2006

Status

approved