A354951 The number of squarefree abundant numbers whose largest prime divisor is prime(n).

0, 0, 1, 3, 5, 13, 27, 59, 125, 257, 534, 1094, 2244, 4607, 9407, 19164, 38939, 79154, 160473, 325213, 658940, 1332598, 2694009, 5440236, 10973874, 22135366, 44644593, 89989907, 181374472, 365371286, 734959945

Offset

1,4

Comments

For n >= 3 we have a(n) >= 2^(n-3) as all squarefree numbers whose largest prime divisor are prime(n) that are a multiple of 6*prime(n) are abundant. - David A. Corneth, Jun 13 2022

Links

Table of n, a(n) for n=1..31.

Example

n  prime(n)  a(n)  terms k of A087248 with A006530(k) = prime(n)
-  --------  ----  ---------------------------------------------
1  2         0     -
2  3         0     -
3  5         1     30
4  7         3     42, 70, 210
5  11        5     66, 330, 462, 770, 2310

Mathematica

a[n_] := Count[Prime[n] * Divisors[Product[Prime[i], {i, 1, n - 1}]], _?(SquareFreeQ[#] && DivisorSigma[-1, #] > 2 &)]; Array[a, 15]

Crossrefs

Cf. A005117, A006530, A087248, A354950.

Sequence in context: A289533 A288827 A084173 * A223645 A190570 A337860

Adjacent sequences: A354948 A354949 A354950 * A354952 A354953 A354954

Keyword

nonn,more

Author

Amiram Eldar, Jun 13 2022

Status

approved