A067929 Numbers k that divide the alternating sum phi(1) - phi(2) + phi(3) - phi(4) + ... + ((-1)^(k+1))*phi(k).

1, 2, 4, 12, 17, 55, 57, 80, 195, 211, 233, 602, 694, 1319, 2726, 26312, 71173, 101457, 145789, 165710, 299228, 483888, 718738, 1757846, 4206121, 9518456, 15505388, 15885915, 15929230, 26445656, 28665696, 37875137, 147389152, 218849960, 430031707, 507418131

Offset: 1

Author

Joseph L. Pe, Feb 22 2002

Keywords

• nonn

Comments

phi(1) - phi(2) + phi(3) - phi(4) = 1 - 1 + 2 - 2 = 0, which is divisible by 4, so 4 is a term of the sequence.

Crossrefs

Cf. A000010, A068773.

Programs

Mathematica

s = 0; Do[s = s + (-1)^(i + 1) * EulerPhi[i]; If[ Mod[s, i] == 0, Print[i]], {i, 1, 10^7}]

PARI

{a067929(m)=local(s,n); s=0; for(n=1,m, if(n%2==0,s=s-eulerphi(n),s=s+eulerphi(n)); if(s%n==0,print1(n,",")))}

Extensions

Edited and extended by Robert G. Wilson v and Klaus Brockhaus, Feb 27 2002

a(27)-a(36) from Donovan Johnson, Jul 26 2011