A351261 a(n) is the largest term encountered on the path to 0 when iterating the map x -> x', and starting from x = A351255(n). Here x' means the arithmetic derivative of x, A003415.

1, 2, 3, 6, 9, 21, 5, 10, 31, 25, 185, 375, 1075, 12575, 7, 14, 21, 42, 165, 70, 105, 318, 365, 1905, 5385, 2175, 2825, 49, 98, 1281, 490, 735, 7287, 2905, 3745, 17747, 16975, 43075, 107150, 370705, 686, 3871, 5145, 29953, 115395, 1001035, 4475975, 11285575, 5145, 115591, 176645, 234955, 40817, 156065, 156065, 1193297

Offset: 1

Author

Antti Karttunen, Feb 11 2022

Keywords

• nonn
• look

Comments

At point n=104776, where a(104776) = 6121569170076203821789253759640129542895524171255601586612637263670135

and A351255(104776) = 144537549602172859330715888995919357193998109417395984504745753750, the ratio a(n)/A351255(n) obtains another record (~ 42352.7947), which motivates a conjecture that it is not bound from above. See also A351079.

Examples

			From A351255(27) = 2625 it takes 12 iterations of map x -> A003415(x) to reach zero: 2625 -> 2825 -> 1155 -> 886 -> 445 -> 94 -> 49 -> 14 -> 9 -> 6 -> 5 -> 1 -> 0. The largest term on this path is 2825, therefore a(27) = 2825.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12878 (computed for all 17-smooth terms of A351255)
• Antti Karttunen, 105368 initial terms, without indices (computed for all 19-smooth terms of A351255, and also for A276086(9699690) = 23)

Crossrefs

Cf. A003415, A276086, A351079, A351255, A351257, A351259.

Programs

PARI

A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i,2]>=f[i,1],return(0), s += f[i, 2]/f[i, 1])); (n*s));
A351079(n) = { my(m=n); while(n>1, n = A003415checked(n); m = max(m,n)); if(n,m); };
for(n=0, 2^9, u=A276086(n); m = A351079(u); if(m>0,print1(m, ", ")));

Formula

a(n) = A351079(A351255(n)).