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

Author

Amiram Eldar, Oct 30 2024

Keywords

• nonn
• easy
• mult

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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... .