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

1,3

Links

Table of n, a(n) for n=1..73.

Formula

Union of A181062 and A002202.

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]]

Prog

(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

Crossrefs

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

Sequence in context: A335042 A257282 A336488 * A080389 A359755 A226038

Adjacent sequences: A221175 A221176 A221177 * A221179 A221180 A221181

Keyword

nonn

Author

Jean-François Alcover, Jan 06 2013

Extensions

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

Status

approved