A048968 Numbers k such that sigma(k) / d(k) is prime.

3, 5, 6, 13, 20, 37, 45, 49, 61, 73, 150, 157, 169, 193, 277, 313, 361, 397, 421, 457, 541, 613, 661, 673, 733, 757, 832, 877, 961, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1445, 1453, 1621, 1657, 1734, 1753, 1849, 1873, 1933, 1993, 2017, 2137, 2341

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn
• nice

Comments

Union of A005383 and A048969.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A000203, A000005, A005383, A048969.

Programs

Maple

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

Mathematica

Select[ Range[2400], PrimeQ[ DivisorSigma[1, #] / DivisorSigma[0, #] ]& ] (* Jean-François Alcover, Sep 24 2012 *)

PARI

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

Extensions

More terms from Jud McCranie