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Numbers k such that sigma(k) / d(k) is prime.
5

%I #36 Jan 13 2025 01:26:54

%S 3,5,6,13,20,37,45,49,61,73,150,157,169,193,277,313,361,397,421,457,

%T 541,613,661,673,733,757,832,877,961,997,1093,1153,1201,1213,1237,

%U 1321,1381,1445,1453,1621,1657,1734,1753,1849,1873,1933,1993,2017,2137,2341

%N Numbers k such that sigma(k) / d(k) is prime.

%C Union of A005383 and A048969.

%H Amiram Eldar, <a href="/A048968/b048968.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)

%p with(numtheory); A048968:=n->`if`(type(sigma(n)/tau(n), prime), n, NULL); seq(A048968(n), n=1..2400); # _Wesley Ivan Hurt_, Feb 04 2014

%t Select[ Range[2400], PrimeQ[ DivisorSigma[1, #] / DivisorSigma[0, #] ]& ] (* _Jean-François Alcover_, Sep 24 2012 *)

%o (PARI) isok(k) = {my(f = factor(k), d = numdiv(f), s = sigma(f)); !(s % d) && isprime(s / d);} \\ _Amiram Eldar_, Jan 13 2025

%Y Cf. A000203, A000005, A005383, A048969.

%K nonn,nice

%O 1,1

%A _G. L. Honaker, Jr._

%E More terms from _Jud McCranie_