The latest PARI/gp command-line and first few lines of ouput are copied below. Note that Keith Briggs has already published in Experimental Mathematics around 2006 on superabundant and colossally abundant numbers out to ~~~ 10^(10^10) or so, using a sieve technique to locate the first ~ 10^9 or 10^10 primes, and making use of the Erdos-Alaoglu formula for the exponents of primes appearing in superabundant and/or colossally abundant numbers …
? for(YYY = 1, 16 , for(ZZZZ=1,5, thebest = 0; www3=vector(100);for(Y=1,100,www3[Y]=www[Y]);stdwww3=vector(dimo);for(Y=1,dimo, stdwww3[Y] = sum(Z=1,30, www3[Z] > (Y-1)));for(Y= ymini+1,yleste , stdwww3[Y] = 0); cst=ratiott(stdwww3); cst=cst-0.00008; for(WW = 1, 1 , for(X=1, lastx , www2=vector(100);for(Y=1,100,www2[Y]=www[Y]);www2[X]=www2[X]+delta[X]; stdwww2=vector(dimo);for(Y=1,dimo, stdwww2[Y] = sum(Z=1,30,www2[Z] > (Y-1))); for(Y=ymini+1,yleste,stdwww2[Y]=0); newr2 = ratiott(stdwww2); if(newr2> cst , print(X,” “, newr2)); if(newr2>cst, cst=newr2; thebest = X) ) ) ; print(“Best: “,thebest,” Score: “,cst); if(thebest>0, www[thebest]=www[thebest]+delta[thebest] ; if(thebest<2, kol = yleste+ delta[1]; sigcpp78k = sigcpp68k*prod(X=yleste+1, kol , 1+prime(X));cpp78k = cpp68k*prod(X= yleste+1 , kol , prime(X));yleste = kol ; sigcpp68k = sigcpp78k; cpp68k = cpp78k) ); dimo = www[1]+ delta[1]+5 ; ) ; print(www) )
1 9999.8161367318480050236360103309064966
Best: 1 Score: 9999.8161367318480050236360103309064966
1 9999.8178667635945587062955380966504143
Best: 1 Score: 9999.8178667635945587062955380966504143
1 9999.8192606775009892371578980177968621
Best: 1 Score: 9999.8192606775009892371578980177968621
1 9999.8210399050758762349397650799650059
Best: 1 Score: 9999.8210399050758762349397650799650059
1 9999.8217474792913918975813952689434803
Best: 1 Score: 9999.8217474792913918975813952689434803
[550805, 495, 55, 19, 10, 7, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
1 9999.8225536547315697620028168239359823
Best: 1 Score: 9999.8225536547315697620028168239359823
1 9999.8229723292895749648920781493140060
Best: 1 Score: 9999.8229723292895749648920781493140060
1 9999.8240274542489694132168978863775870
Best: 1 Score: 9999.8240274542489694132168978863775870
1 9999.8259825043472576022761466011125380
