A270807
Trajectory of 1 under the map n -> n + n/gpf(n) + 1 (see A269304).
Original entry on oeis.org
1, 3, 5, 7, 9, 13, 15, 19, 21, 25, 31, 33, 37, 39, 43, 45, 55, 61, 63, 73, 75, 91, 99, 109, 111, 115, 121, 133, 141, 145, 151, 153, 163, 165, 181, 183, 187, 199, 201, 205, 211, 213, 217, 225, 271, 273, 295, 301, 309, 313, 315, 361, 381, 385, 421, 423, 433, 435, 451, 463, 465
Offset: 1
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gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
lista(nn) = {a = 1; for (n=1, nn, print1(a, ", "); a = a + a/gpf(a) + 1;);} \\ Michel Marcus, Apr 06 2016
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from _future_ import division
from sympy import primefactors
A270807_list, b = [], 1
for i in range(10000):
A270807_list.append(b)
b += b//(max(primefactors(b)+[1])) + 1 # Chai Wah Wu, Apr 06 2016
A329288
Table T(n,k) read by antidiagonals: T(n,k) = f(T(n,k)) starting with T(n,1)=n, where f(x) = x - 1 + x/gpf(x), that is, f(x) = A269304(x)-2.
Original entry on oeis.org
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 5, 5, 1, 2, 3, 5, 5, 6, 1, 2, 3, 5, 5, 7, 7, 1, 2, 3, 5, 5, 7, 7, 8, 1, 2, 3, 5, 5, 7, 7, 11, 9, 1, 2, 3, 5, 5, 7, 7, 11, 11, 10, 1, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 1, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 12
Offset: 1
Table begins:
1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, ...
3, 3, 3, 3, 3, ...
4, 5, 5, 5, 5, ...
5, 5, 5, 5, 5, ...
6, 7, 7, 7, 7, ...
7, 7, 7, 7, 7, ...
8, 11, 11, 11, 11, ...
9, 11, 11, 11, 11, ...
10, 11, 11, 11, 11, ...
11, 11, 11, 11, 11, ...
12, 15, 17, 17, 17, ...
13, 13, 13, 13, 13, ...
14, 15, 17, 17, 17, ...
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Clear[f,it,order,seq]; f[n_]:=f[n]=n-1+n/FactorInteger[n][[-1]][[1]]; it[k_,n_]:=it[k,n]=f[it[k,n-1]]; it[k_,1]=k; SetAttributes[f,Listable]; SetAttributes[it,Listable]; it[#,Range[10]]&/@Range[800]
A271418
Define a sequence by b(1) = n, b(m) = b(m-1) + b(m-1)/A052126(m) + 1; then a(n) is the least m such that b(m) belongs to A270807.
Original entry on oeis.org
1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 4, 1, 2, 3, 4, 1, 3, 1, 4, 2, 4, 1, 4, 1, 4, 4, 4, 3, 2, 2, 3, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 1, 3, 3, 2, 3, 2, 2, 3, 2, 3, 1, 4, 1
Offset: 1
the sequence where b(1) = 2 is 2, 4, 7, 9, 13, 15, ...
7 is shared with A270807
there are 3 terms in 2, 4, 7; a(2) = 3
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f[n_] := n + n/FactorInteger[n][[-1, 1]] + 1; s = NestList[f, 1, 10^2]; Table[Length@ NestWhileList[f, n, ! MemberQ[s, #] &], {n, 120}] (* Michael De Vlieger, Apr 08 2016 *)
Showing 1-3 of 3 results.
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