cp's OEIS Frontend

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))).

%I A049057 #12 Mar 11 2021 03:17:39
%S A049057 20,40,52,60,104,120,156,312,480,488,780,1248,1464,1560,5856,6240,
%T A049057 7320,7680,8168,9744,13260,19968,24504,26520,29280,93696,98016,99840,
%U A049057 106080,122520,124440,468480,490080,497760,1568256,1697280,2082840,7841280
%N 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))).
%C A049057 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
%C A049057 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
%C A049057 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
%e A049057 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.
%e A049057 (r,s,t)=(20,20,20), (40,52,60), (52,60,40), (60,40,52), (104,156,120), (120,104,156), ..., (29280,29280,29280).
%o A049057 (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
%Y A049057 Cf. A049058, A049059, A049060.
%K A049057 nonn
%O A049057 0,1
%A A049057 _Yasutoshi Kohmoto_
%E A049057 Corrected and extended by _R. J. Mathar_, Oct 12 2006