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A278373 Numbers of the form sigma(k) + phi(k) - 2k. 6

%I #27 Dec 10 2016 00:23:31

%S 0,1,2,3,4,6,7,8,9,10,12,13,14,15,16,17,18,20,22,24,25,26,28,29,30,31,

%T 32,34,36,37,38,40,41,42,44,46,48,49,50,52,54,56,57,58,60,61,62,63,64,

%U 65,66,68,70,72,73,74,75,76,77,78,80,82,84,85,86,88,89,90,91,92,93,94,96,97,98,100,102,104,106,108,109,110,111,112,114

%N Numbers of the form sigma(k) + phi(k) - 2k.

%C Empirically, every integer n >= 18 is of the form n = p+q+r for distinct primes p,q,r. If true, then every even number e >= 36 is this sequence, since e = 2(p+q+r) = sigma(pqr) + phi(pqr) - 2pqr, which implies all even e >= 0 are in this sequence.

%H David W. Wilson, <a href="/A278373/b278373.txt">Table of n, a(n) for n = 1..10000</a>

%t Take[#, 85] &@ Union@ Table[DivisorSigma[1, n] + EulerPhi@ n - 2 n, {n, 10^4}] (* _Michael De Vlieger_, Nov 30 2016 *)

%Y Smallest k with sigma(k) + phi(k) - 2k = a(n) is A278374(n).

%Y Complement is A056996.

%Y Sequence A051709 sorted into ascending order, with duplicates removed.- _Antti Karttunen_, Dec 09 2016

%Y Cf. A000010 (phi), A000203 (sigma).

%K nonn

%O 1,3

%A _David W. Wilson_, Nov 19 2016

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Last modified March 29 02:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)