A049057 First element r of (-1)sigma sociable triple (r,s,t): s=(-1)sigma(r), t=(-1)sigma(s), r=(-1)sigma(t), 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))).

20, 40, 52, 60, 104, 120, 156, 312, 480, 488, 780, 1248, 1464, 1560, 5856, 6240, 7320, 7680, 8168, 9744, 13260, 19968, 24504, 26520, 29280, 93696, 98016, 99840, 106080, 122520, 124440, 468480, 490080, 497760, 1568256, 1697280, 2082840, 7841280

Offset: 0

Author

Yasutoshi Kohmoto

Keywords

• nonn

Comments

Since the definition is circular and the definition does not specify that r is the largest number in the triple, for each r in the sequence also the s and t show up. - R. J. Mathar, Oct 12 2006

Otherwise, if the definition is supposed to mean "smallest r of a triple....", the list is 20, 40, 104, 312, 480, 1248, 5856, 7680, 9744, 19968, 29280, ... - R. J. Mathar, Oct 12 2006

If, as a third interpretation, the sequence is "Smallest r of a triple of pairwise different numbers r,s,t with..." then the sequence is 40, 104, 480, 1248, 5856, 7680, ... - R. J. Mathar, Oct 12 2006

Examples

			Factorizations 2^3*5, 2^3*13, 2^3*61, 2^3*3*5*13, 2^3*1021, 2^3*3*5*13*17, 2^5*3*5*17*61.
(r,s,t)=(20,20,20), (40,52,60), (52,60,40), (60,40,52), (104,156,120), (120,104,156), ..., (29280,29280,29280).
		

Crossrefs

Cf. A049058, A049059, A049060.

Programs

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) ; } isA049057(r)={ local(s,t) ; s=A049060(r) ; t=A049060(s) ; if( r == A049060(t), return(1), return(0) ) ; } { for(n=1,30000000, if( isA049057(n), print(n," ",factor(n)) ) ; ) ; } \\ R. J. Mathar, Oct 12 2006

Extensions

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