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A097296
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Numbers k such that A001055(k) divides k.
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4
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1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 17, 19, 20, 22, 23, 26, 27, 28, 29, 30, 31, 34, 36, 37, 38, 41, 43, 44, 46, 47, 48, 52, 53, 56, 58, 59, 61, 62, 67, 68, 70, 71, 73, 74, 76, 79, 82, 83, 86, 89, 92, 94, 97, 101, 103, 105, 106, 107, 109, 110, 113, 116, 118, 122, 124, 127, 130
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OFFSET
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1,2
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LINKS
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FORMULA
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Luca et al. estimate the density of this sequence (see their Theorem 3).
The number of terms that do not exceed x is ~ x/(log(x))^(1+o(1)) (Luca et al., 2008). - Amiram Eldar, May 23 2024
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MAPLE
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g:= proc(n, k) option remember; `if`(n>k, 0, 1)+
`if`(isprime(n), 0, add(`if`(d>k, 0, g(n/d, d)),
d=numtheory[divisors](n) minus {1, n}))
end:
a:= proc(n) option remember; local k;
for k from 1+`if`(n=1, 0, a(n-1))
while irem(k, g(k$2))>0 do od; k
end:
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MATHEMATICA
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g[n_, k_] := g[n, k] = If[n > k, 0, 1] + If[PrimeQ[n], 0, Sum[If[d > k, 0, g[n/d, d]], {d, Divisors[n] // Most // Rest}]]; a[1] = 1; a[n_] := (For[k = 1 + If[n == 1, 0, a[n-1]], Mod[k, g[k, k]] > 0 , k++]; k); Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 07 2014, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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