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

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

Offset: 1

Author

David W. Wilson, Nov 19 2016

Keywords

• nonn

Comments

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.

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

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

Complement is A056996.

Sequence A051709 sorted into ascending order, with duplicates removed.- Antti Karttunen, Dec 09 2016

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

Programs

Mathematica

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