A333646 Numbers k divisible by the largest prime factor of the sum of divisors of k; a(1) = 1.

1, 6, 15, 28, 30, 33, 40, 42, 51, 66, 69, 84, 91, 95, 102, 105, 117, 120, 135, 138, 140, 141, 145, 159, 165, 182, 186, 190, 210, 213, 224, 231, 234, 255, 270, 273, 280, 282, 285, 287, 290, 295, 308, 318, 321, 330, 345, 357, 364, 395, 420, 426, 435, 440, 445, 455

Offset: 1

Author

Amiram Eldar, Jun 05 2020

Keywords

• nonn

Comments

Pomerance (1973) proved that all the harmonic numbers (A001599) are in this sequence.

If m is a product of distinct Mersenne primes (A046528), m > 1 and 3 | m, then 2*m is a term.

If p is a term of A005105 then, 6*p is a term for p > 3, and 3*p is a term if p is not a Mersenne prime (A000668).

Examples

			15 is a term since sigma(15) = 24, 3 is the largest prime factor of 24, and 15 is divisible by 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Carl Pomerance, On a Problem of Ore: Harmonic Numbers, unpublished manuscript, 1973; abstract *709-A5, Notices of the American Mathematical Society, Vol. 20, 1973, page A-648, entire volume.

Crossrefs

A001599 and A105402 are subsequences.

Cf. A000203, A000668, A005105, A006530, A046528, A071190.

Programs

Mathematica

Select[Range[500], Divisible[#, FactorInteger[DivisorSigma[1, #]][[-1, 1]]] &]

Formula

Numbers k such that A071190(k) | k.