A376122 Abundance of primitive abundant numbers.

2, 4, 4, 2, 14, 12, 8, 2, 16, 32, 2, 16, 8, 30, 26, 22, 20, 164, 16, 74, 10, 148, 4, 2, 28, 140, 36, 116, 100, 124, 232, 68, 224, 100, 20, 92, 558, 208, 20, 212, 4, 68, 546, 208, 60, 184, 52, 56, 54, 176, 44, 196, 48, 28, 44, 128, 522, 188, 152, 38, 112, 354, 4

Offset

1,1

Comments

A number k is abundant if sigma(k) > 2k (cf. A005101), and deficient (A005100) if sigma(k) < 2k. An abundant number is considered primitive (A071395) if all its proper divisors are deficient numbers.

Links

Danko Alorvor, Table of n, a(n) for n = 1..10000

Formula

a(n) = A033880(A071395(n)).

Example

2 is a term since the proper divisors of 20 (1, 2, 4, 5, and 10) are all deficient numbers and their sum equals 22, hence the abundance of 20 is 22 - 20 = 2.

Prog

(Python) from sympy import is_abundant, proper_divisors, is_deficient
def primitives_abundances(stop):
    abundances = []
    for n in range(1, stop + 1):
        if is_abundant(n):
            divisors = proper_divisors(n)
            if all(is_deficient(divisor) for divisor in divisors):
                abundances.append(sum(divisors) - n)
    return abundances

Crossrefs

Subset of A033881. Cf. A033880, A071395.

Sequence in context: A193028 A203631 A188424 * A220588 A346262 A185356

Adjacent sequences: A376119 A376120 A376121 * A376123 A376124 A376125

Keyword

nonn,easy

Author

Danko Alorvor, Sep 11 2024

Status

approved