A221178 Union of (prime powers minus 1) and values of Euler totient function.

0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 15, 16, 18, 20, 22, 24, 26, 28, 30, 31, 32, 36, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 63, 64, 66, 70, 72, 78, 80, 82, 84, 88, 92, 96, 100, 102, 104, 106, 108, 110, 112, 116, 120, 124, 126, 127, 128, 130, 132, 136, 138, 140, 144, 148, 150, 156, 160, 162, 164, 166, 168, 172, 176

Offset: 1

Author

Jean-François Alcover, Jan 06 2013

Keywords

• nonn

Crossrefs

Cf. A000010, A002202, A000961, A181062, A070932 (multiplicative closure).

Programs

Mathematica

max = 200;
selNu = Select[Range[max], PrimeNu[#] == 1&]-1;
phiQ[m_] := Select[Range[m+1, 2*m*Product[1/(1-1/(k*Log[k])), {k, 2, DivisorSigma[0, m]}]], EulerPhi[#] == m&, 1] != {};
selPhi = Select[Range[max], phiQ];
Join[{0}, Union[selNu, selPhi]]

PARI

list(lim)=my(P=1, q, v, u=List([0])); forprime(p=2, default(primelimit), if(eulerphi(P*=p)>=lim, q=p; break)); v=vecsort(vector(P/q*lim\eulerphi(P/q), k, eulerphi(k)), , 8); v=select(n->n<=lim, v); forprime(p=2,sqrtint(lim\1+1),P=p;while((P*=p) <= lim+1, listput(u, P-1))); vecsort(concat(v, Vec(u)),,8) \\ Charles R Greathouse IV, Jan 08 2013

Formula

Union of A181062 and A002202.

Extensions

Edited by N. J. A. Sloane, Jan 06 2013