A377515 The largest divisor of n that is a term in A276078.

1, 2, 3, 2, 5, 6, 7, 2, 9, 10, 11, 6, 13, 14, 15, 2, 17, 18, 19, 10, 21, 22, 23, 6, 25, 26, 9, 14, 29, 30, 31, 2, 33, 34, 35, 18, 37, 38, 39, 10, 41, 42, 43, 22, 45, 46, 47, 6, 49, 50, 51, 26, 53, 18, 55, 14, 57, 58, 59, 30, 61, 62, 63, 2, 65, 66, 67, 34, 69, 70

Offset

1,2

Comments

First differs from A327937 at n = 625 = 5^4: a(625) = 125, while A327937(625) = 625.

The number of these divisors is A377516(n), and their sum is A377517(n).

Links

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

Formula

Multiplicative with a(p^e) = p^min(pi(p), e), where pi(n) = A000720(n).

a(n) = n if and only if n is in A276078.

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

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - 1/(p^pi(p) * (p+1))) = 0.80906238421914194523... .

Mathematica

f[p_, e_] := p^Min[PrimePi[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(primepi(f[i, 1]), f[i, 2])); }

Crossrefs

Cf. A000720, A276078, A327937, A377516, A377517, A377518.

Sequence in context: A090078 A325814 A325126 * A327937 A259445 A080979

Adjacent sequences: A377512 A377513 A377514 * A377516 A377517 A377518

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 30 2024

Status

approved