A329660 Numbers m such that sigma(m) is a Lucas number (A000032), where sigma(m) is the sum of divisors of m (A000203).

1, 2, 3, 4, 10, 17, 688, 1075, 103681, 7860997, 10749957121, 115561578124838522881, 488296733939737583689, 489501979450313254561, 3628116960730713370000, 8784132317383836036997, 8784200214538920269317, 50755107290462736080376601, 94426187701102977738552612783157

Offset: 1

Author

Amiram Eldar, Nov 18 2019

Keywords

• nonn

Comments

Prime numbers of the form L(k)-1, where L(k) is the k-th Lucas number, are in this sequence. The terms 2, 3, 17, 103681, and 10749957121 are primes of this form (with k = 2, 3, 6, 24, 48). Also in the sequence is the prime L(96) - 1 = 115561578124838522881.

Examples

			4 is in the sequence since sigma(4) = 7 is a Lucas number.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..225

Crossrefs

Cf. A000032, A000203, A272412.

Programs

Mathematica

f = LucasL @ Range[1, 40]; Select[Range[10^6], MemberQ[f, DivisorSigma[1, #]] &]  (* after Giovanni Resta at A272412 *)

Extensions

a(12)-a(19) from Giovanni Resta, Nov 18 2019