A392651 Odd solid numbers that are not odd primitive abundant numbers. A number k is solid if a subset of its sum-irreducible nontrivial divisors sums to k. Sum-irreducible divisors are defined in A392650.

53235, 91035, 101115, 103005, 106785, 109395, 113715, 120015, 122265, 123795, 129465, 131355, 140805, 142695, 148005, 148365, 154035, 157815, 159885, 163485, 166005, 166635, 168525, 169155, 171045, 171675, 173565, 177975, 180495, 182385, 185535, 186165, 186615

Offset

1,1

Comments

[In A195101 the author also refers to his numbers as 'solid numbers'. These are unrelated to the numbers presented here.]

Links

Table of n, a(n) for n=1..33.

Example

n = 53235 is a term of this sequence, because 3 + 7 + 315 + 845 + 1183 + 1365 + 1521 + 2535 + 3549 + 5915 + 7605 + 10647 + 17745 = 53235. All summands are divisors of n and sum-irreducible.

Prog

(SageMath)
# The function 'is_sum_irreducible' is defined in A392650.
# The function 'subset_sum_exists' is defined in A392652.
def is_A392651(n) -> bool:
    if n < 53235 or n % 2 == 0: return False
    divs = divisors(n)[1:-1]
    irr_divs = [d for d in divs if is_sum_irreducible(d)]
    return subset_sum_exists(irr_divs, n)
A = [n for n in range(1, 186616) if is_A392651(n)]; print(A)

Crossrefs

Cf. A006038, A392649, A392650, A392652.

Sequence in context: A155557 A015315 A061330 * A195656 A195651 A294752

Adjacent sequences: A392648 A392649 A392650 * A392652 A392653 A392654

Keyword

nonn

Author

Peter Luschny, Feb 02 2026

Status

approved