A280590 - OEIS

%I #26 Apr 09 2020 12:23:12

%S 1,3,5,6,11,17,24,26,27,29,38,41,59,71,101,107,125,137,149,158,179,

%T 191,197,206,218,227,239,269,281,311,344,347,419,431,446,458,461,521,

%U 536,569,599,617,641,659,698,809,821,827,857,878,881,1019,1031,1049,1061

%N Numbers k such that for any positive integers (a, b), if a * b = k then sigma(a) + sigma(b) is a prime.

%C The subsequence of primes {3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, ... is exactly A001359 (lesser of twin primes).

%H Amiram Eldar, <a href="/A280590/b280590.txt">Table of n, a(n) for n = 1..10000</a>

%e 1 is in the sequence because 1 = 1*1 and sigma(1) + sigma(1) = 1 + 1 = 2 is prime.

%e 24 is in the sequence because A038548(24) = 4 => four decompositions of 24 = 1*24 = 2*12 = 3*8 = 4*6 and

%e sigma(1) + sigma(24) =  1 + 60 = 61 is prime;

%e sigma(2) + sigma(12) =  3 + 28 = 31 is prime;

%e sigma(3) + sigma(8)  =  4 + 15 = 19 is prime;

%e sigma(4) + sigma(6)  =  7 + 12 = 19 is prime.

%t t={};Do[ds=Divisors[n];If[EvenQ[Length[ds]],ok=True;k=1;While[k<=Length[ds]/2&&(ok=PrimeQ[DivisorSigma[1,ds[[k]]]+DivisorSigma[1,ds[[-k]]]]),k++];If[ok,AppendTo[t,n]]],{n,2,4000}];t

%o (PARI) isok(n) = {fordiv(n, d, if (d^2 <= n, if (! isprime(sigma(d) + sigma(n/d)), return (0)););); return(1);} \\ _Michel Marcus_, Jan 06 2017

%Y Cf. A000203, A001359, A038548, A080715.

%K nonn

%O 1,2

%A _Michel Lagneau_, Jan 06 2017