|
%I #16 Apr 04 2024 07:55:45
%S 1,3,14,35,42,105,209,248,297,418,594,627,744,1045,1254,1485,1736,
%T 2926,3135,3339,3596,3689,3956,4064,4158,5208,5396,5890,6461,7315,
%U 7668,8370,8636,8680,8778,8932,9875,10013,10395,10788,11067,11687
%N Numbers k such that phi(k)*d(k) is a multiple of sigma(k), where d(k) is the number of divisors of k.
%C Equality holds for 1, 3, 14, 42 and no others < 4290000000.
%H Amiram Eldar, <a href="/A050934/b050934.txt">Table of n, a(n) for n = 1..10000</a>
%e phi(35)*d(35) = 4*24, a multiple of sigma(35) = 48, so 35 is in the sequence.
%t Select[Range[12000],Divisible[EulerPhi[#]DivisorSigma[0,#], DivisorSigma[ 1,#]]&] (* _Harvey P. Dale_, Jan 11 2019 *)
%o (PARI) is(n) = {my(f = factor(n)); !((eulerphi(f) * numdiv(f)) % sigma(f));} \\ _Amiram Eldar_, Apr 04 2024
%Y Cf. A000005 (d), A000010 (phi), A000203 (sigma).
%K nonn
%O 1,2
%A _Jud McCranie_, Dec 30 1999
|
