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

1,1

Links

Table of n, a(n) for n=1..26.

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.

Example

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

Prog

(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

Crossrefs

Cf. A002025, A002046, A014688, A259180.

Sequence in context: A043986 A124967 A224443 * A261259 A168348 A052032

Adjacent sequences: A349776 A349777 A349778 * A349780 A349781 A349782

Keyword

nonn

Author

Michel Marcus, Nov 30 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

Status

approved