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A349779
Pairs of integers i,j such that i+prime(i) and j+prime(j) are a pair of amicable numbers.
0
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
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
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