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

Author

Amiram Eldar, Jun 13 2022

Keywords

• nonn
• more

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

Examples

			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
		

Crossrefs

Cf. A005117, A006530, A087248, A354950.

Programs

Mathematica

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