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A307081 Triangular array read by rows: row n consists of the numbers k from 1 to n sorted in ascending order according to the value of f(k) = A095112(k)/k. 2
1, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 5, 3, 2, 4, 1, 5, 3, 2, 4, 6, 1, 7, 5, 3, 2, 4, 6, 1, 7, 5, 3, 2, 4, 6, 8, 1, 7, 5, 3, 9, 2, 4, 6, 8, 1, 7, 5, 3, 9, 2, 10, 4, 6, 8, 1, 11, 7, 5, 3, 9, 2, 10, 4, 6, 8, 1, 11, 7, 5, 3, 9, 2, 10, 4, 6, 8, 12, 1, 13, 11, 7, 5, 3, 9, 2, 10, 4, 6, 8, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
f(n) = Sum_{p prime divisor of n} Sum{i=1..v_p(n)} 1/p^i, where v_p denotes the p-adic valuation. f is injective.
LINKS
EXAMPLE
Array begins:
1
1 2
1 3 2
1 3 2 4
1 5 3 2 4
1 5 3 2 4 6
1 7 5 3 2 4 6
1 7 5 3 2 4 6 8
1 7 5 3 9 2 4 6 8
1 7 5 3 9 2 10 4 6 8
1 11 7 5 3 9 2 10 4 6 8
1 11 7 5 3 9 2 10 4 6 8 12
1 13 11 7 5 3 9 2 10 4 6 8 12
...
MATHEMATICA
f[n_]:=If[n==1, 0, Plus@@(Sum[1/#[[1]]^i, {i, #[[2]]}]&)/@FactorInteger[n]]
row[n_]:=SortBy[Range[n], f]
For[n=1, n<=13, n++, r=row[n]; For[i=1, i<=n, i++, WriteString["stdout", r[[i]], ", "]]]
PROG
(PARI) f(n) = sumdiv(n, d, (1==omega(d))*(n/d)); \\ A095112
cmpf(na, nb) = f(na)/na-f(nb)/nb;
tabl(nn) = {for (n=1, nn, print(Vec(vecsort([1..n], cmpf, 1))); ); } \\ Michel Marcus, Mar 28 2019
CROSSREFS
Sequence in context: A085014 A082074 A132283 * A256440 A088370 A328719
KEYWORD
nonn,tabl
AUTHOR
Luc Rousseau, Mar 23 2019
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)