A173494 Numbers m such that no square greater than 1 can be written as sum of distinct divisors of m.

1, 2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 38, 41, 43, 47, 53, 58, 59, 61, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 86, 89, 91, 97, 101, 103, 106, 107, 109, 113, 127, 131, 133, 134, 137, 139, 145, 146, 149, 151, 157, 163, 167, 173, 178, 179, 181, 185, 187, 191, 193, 197

Offset

1,2

Comments

2546 is the smallest term having more than two prime factors: 2546 = 2*19*67.

Links

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

Formula

A173493(a(n)) = 1.

Mathematica

q[m_] := Module[{d = Divisors[m], sum, sq, x}, sum = Plus @@ d; sq = Range[2, Floor[Sqrt[sum]]]^2; Total[CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sq]]] == 0]; Select[Range[200], q] (* Amiram Eldar, Apr 16 2025 *)

Crossrefs

Cf. A173493.

A045344 is a subsequence (the primes except 3).

Sequence in context: A081259 A177512 A118751 * A137519 A045344 A087685

Adjacent sequences: A173491 A173492 A173493 * A173495 A173496 A173497

Keyword

nonn

Author

Reinhard Zumkeller, Feb 20 2010

Status

approved