A380090 The sum of the unitary divisors of n that are terms in A207481.

1, 3, 4, 5, 6, 12, 8, 1, 10, 18, 12, 20, 14, 24, 24, 1, 18, 30, 20, 30, 32, 36, 24, 4, 26, 42, 28, 40, 30, 72, 32, 1, 48, 54, 48, 50, 38, 60, 56, 6, 42, 96, 44, 60, 60, 72, 48, 4, 50, 78, 72, 70, 54, 84, 72, 8, 80, 90, 60, 120, 62, 96, 80, 1, 84, 144, 68, 90, 96

Offset

1,2

Comments

First differs from A371242 at n = 27.

Links

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

Formula

a(n) = A034448(A380088(n)).

Multiplicative with a(p^e) = p^e + 1 if e <= p, and 1 otherwise.

a(n) = 1 if and only if n is in A054743.

a(n) < A034448(n) if and only if n is in A185359.

a(n) = A034448(n) if and only if n is in A207481.

a(n) = A377520(n) if and only if n is squarefree (A005117).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (p^(p+2) + p^(p+1) + p^p - p - 1)/(p^(p+1) * (p+1)) = 1.2078161... .

Mathematica

f[p_, e_] := If[e <= p, p^e, 0] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] <= f[i, 1], f[i, 1]^f[i, 2], 0) + 1); }

Crossrefs

Cf. A005117, A054743, A077610, A185359, A207481, A371242, A377520, A380087, A380088, A380089.

Sequence in context: A103402 A154664 A371242 * A366743 A191750 A346613

Adjacent sequences: A380087 A380088 A380089 * A380091 A380092 A380093

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 12 2025

Status

approved