A096847 Numbers n such that A094471(n) is prime.

3, 4, 8, 36, 100, 128, 324, 400, 1296, 1600, 1936, 2116, 3364, 4356, 10404, 11236, 20736, 22500, 26244, 27556, 28900, 30976, 38416, 40000, 52900, 53824, 57600, 60516, 88804, 93636, 107584, 108900, 115600, 123904, 125316, 129600, 211600

Offset

1,1

Comments

Old name was "Solutions to {A094471[x]=prime} that is to {x; x*tau[x]-sigma[x]=prime}."

All terms after the first are even, because A094471(n) is even if n is odd. The first term == 2 (mod 4) is a(135) = 9653618. - Robert Israel, Nov 11 2015

Links

Harvey P. Dale, Table of n, a(n) for n = 1..100

Example

n=8: 8*tau[8]-sigma[8]=8*4-15=32-15=17 is a prime, so 8 is here.

Maple

A094471:= n -> n*numtheory:-tau(n) - numtheory:-sigma(n):
select(t -> isprime(A094471(t)), 2*[3/2, $1..10^6]); # Robert Israel, Nov 11 2015

Mathematica

Do[s=n*DivisorSigma[0, n]-DivisorSigma[1, n]; If[PrimeQ[s], Print[{n, s}]; ta[[u]]=n; tb[[u]]=s; u=u+1], {n, 1, 1000000}]; ta
Select[Range[215000], PrimeQ[# DivisorSigma[0, #]-DivisorSigma[1, #]]&] (* Harvey P. Dale, Dec 07 2021 *)

Prog

(PARI) isok(n) = isprime(n*numdiv(n)-sigma(n)); \\ Michel Marcus, Nov 12 2015

Crossrefs

Cf. A094471, A096848.

Sequence in context: A366812 A180629 A258372 * A367131 A011993 A286125

Adjacent sequences: A096844 A096845 A096846 * A096848 A096849 A096850

Keyword

nonn

Author

Labos Elemer, Jul 15 2004

Extensions

Name modified by Tom Edgar, Nov 12 2015

Status

approved