A349779 Pairs of integers i,j such that i+prime(i) and j+prime(j) are a pair of amicable numbers.

41, 51, 99525, 104283, 280899, 295869, 18378754, 21937204, 52084243, 53107499, 163148785, 166346021, 179162279, 183252051, 212063283, 244033955, 3731366783, 4226663091, 7134801326, 7818930716, 10469380661, 12074408463, 12445587194, 12667334246, 16055012737, 17258948163

Offset: 1

Author

Michel Marcus, Nov 30 2021

Keywords

• nonn

Examples

			41 + prime(41) = 41 + 179 = 220, 51 + prime(51) = 51 + 233 = 284, and (220, 284) is an amicable pair.
		

Links

• Juan Luis Varona, On the Solution of the Equation n = a*k + b*p_k by Means of an Iterative Method, Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.5.

Crossrefs

Cf. A002025, A002046, A014688, A259180.

Programs

Python

from sympy import nextprime, divisor_sigma
d = dict()
j, p = 0, 0
while True:
    j, p = j+1, nextprime(p)
    n = j+p
    a = divisor_sigma(n)-n
    d[(n, a)] = j
    if (a, n) in d:
        print(d[(a, n)], j) # Martin Ehrenstein, Dec 02 2021

Extensions

a(7)-a(8) from Amiram Eldar, Nov 30 2021

a(9)-a(16) from Michel Marcus, Dec 01 2021

a(17)-a(26) from Martin Ehrenstein, Dec 03 2021