

A278373


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


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


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


MATHEMATICA

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


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).
Sequence in context: A028392 A175970 A286689 * A183293 A184524 A047226
Adjacent sequences: A278370 A278371 A278372 * A278374 A278375 A278376


KEYWORD

nonn


AUTHOR

David W. Wilson, Nov 19 2016


STATUS

approved



