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A221178 Union of (prime powers minus 1) and values of Euler totient function. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A226038 A181062

Adjacent sequences:  A221175 A221176 A221177 * A221179 A221180 A221181

KEYWORD

nonn

AUTHOR

Jean-Fran├žois Alcover, Jan 06 2013

EXTENSIONS

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

STATUS

approved

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Last modified November 25 13:38 EST 2020. Contains 338623 sequences. (Running on oeis4.)