A377518 The largest divisor of n that is a term in A207481.

1, 2, 3, 4, 5, 6, 7, 4, 9, 10, 11, 12, 13, 14, 15, 4, 17, 18, 19, 20, 21, 22, 23, 12, 25, 26, 27, 28, 29, 30, 31, 4, 33, 34, 35, 36, 37, 38, 39, 20, 41, 42, 43, 44, 45, 46, 47, 12, 49, 50, 51, 52, 53, 54, 55, 28, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66, 67, 68, 69

Offset

1,2

Comments

The number of these divisors is A377519(n), and their sum is A377520(n).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = p^min(p, e).

a(n) = n if and only if n is in A207481.

Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (p^((p+1)*s) - p^(p+1) - p^(p*s) + p^p)/p^((p+1)*s).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - 1/(p^p * (p+1))) = 0.908130438292447963703... .

Mathematica

f[p_, e_] := p^Min[p, e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^min(f[i, 1], f[i, 2])); }

Crossrefs

Cf. A207481, A368329, A377515, A377519, A377520.

Sequence in context: A083501 A007922 A007948 * A355261 A353897 A366905

Adjacent sequences: A377515 A377516 A377517 * A377519 A377520 A377522

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 30 2024

Status

approved