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Primes of the form highly abundant number - 1.
3

%I #10 Jun 07 2019 08:19:25

%S 2,3,5,7,11,17,19,23,29,41,47,59,71,83,89,107,167,179,239,359,419,479,

%T 503,599,659,719,839,1259,1439,1559,1619,1979,2099,2339,2399,2879,

%U 3023,3119,3359,3779,4679,5039,5879,6299,6719,7559,7919,8819,9239,10079,12239,13859,21839,22679,35279

%N Primes of the form highly abundant number - 1.

%C Note that this sequence and A181561 have an intersection beginning {2, 3, 5, 7, 11, 17, 19, ...}. This sequence UNION A181561 might be called nearly highly abundant primes. That union begins: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 71, 73, 83, 89, 97, 107, 109, 167, 179, 181, 211, 239, 241, 337, 359, 419, 421, 479, 503, 541, 599, 601, 631, 659, 661, 719, 839, 1009, 1201, 1439, 1559, 1619, 1621, 1979, 1801, 2099} and thus has twin nearly highly abundant prime pairs: {(3,5), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73), (107,109), (179,181), (239,241), (419,421), (599,601), (659,661), (1619,1621), ...}.

%H Amiram Eldar, <a href="/A181562/b181562.txt">Table of n, a(n) for n = 1..1588</a>

%F {A002093(i) - 1} INTERSECTION A000040.

%F {(sigma(n) > sigma(m) for all m < n) - 1} INTERSECTION A000040.

%e The 55th highly abundant number is 2100; subtract one to get 2099, which is prime.

%t seq = {}; smax = 0; Do[s = DivisorSigma[1, n]; If[s > smax, smax = s; If[PrimeQ[n - 1], AppendTo[seq, n - 1]]], {n, 1, 10^4}]; seq (* _Amiram Eldar_, Jun 07 2019 *)

%Y Cf. A000040, A000203, A002093, A181561.

%K nonn,easy

%O 1,1

%A _Jonathan Vos Post_, Jan 29 2011