A240960 Numbers m such that sigma(m) - phi(m) = tau(m)^omega(m), where sigma=A000203, phi=A000010, tau=A000005 and omega=A001221.

2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 1

Author

Reinhard Zumkeller, Aug 05 2014

Keywords

• nonn

Comments

a(n) = A182140(n) for n <= 35.

All primes p are in the sequence since (p+1) - (p-1) = 2^1. The first composites are 15, 119748396, 139254850, 187768485, 1420027536, 3991789984. A182140 seems unrelated. - Jens Kruse Andersen, Aug 05 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000010, A000203, A001221, A051612, A110088, A182140, A110086.

Programs

Haskell

a240960 n = a240960_list !! (n-1)
a240960_list = filter (\x -> a051612 x == a110088 x) [1..]

Maple

with(numtheory):
filter:= n -> sigma(n) - phi(n) = tau(n)^nops(factorset(n)):
select(filter, [$1..1000]); # Robert Israel, Aug 05 2014

Mathematica

Select[Range[300], DivisorSigma[1, #] - EulerPhi[#] == DivisorSigma[0, #]^PrimeNu[#]&] (* Jean-François Alcover, Mar 08 2019 *)

PARI

is(n)=my(f=factor(n)); sigma(f)-eulerphi(f)==numdiv(f)^omega(f) \\ Charles R Greathouse IV, Nov 26 2014

Python

from sympy import totient,divisors,divisor_count,primefactors
filter(lambda x:sum(divisors(x))-totient(x)==divisor_count(x)**len(primefactors(x)), range(1,10**5)) # Chai Wah Wu, Aug 05 2014