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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.
8
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
1,2
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.
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)
FORMULA
a(n) = A351079(A351255(n)).
EXAMPLE
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.
PROG
(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, ", ")));
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Feb 11 2022
STATUS
approved