A163378 -id:A163378 - cp's OEIS frontend

A163109 a(n) = phi(tau(n)).

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 2, 6, 2, 4, 1, 2, 2, 4, 1, 4, 1, 2, 2, 2, 2, 4, 1, 4, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 2, 2, 2, 2, 4, 1, 2, 2, 6, 1, 4, 1, 4, 4

Offset: 1

Jaroslav Krizek, Jul 20 2009

			a(16) = a(2^(5-1)) = 5-1 = 4.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n

Cf. A000005, A000010, A062821, A163377, A163378, A163379.

Table[EulerPhi[DivisorSigma[0, n]], {n, 1, 80}] (* Carl Najafi, Aug 15 2011 *)

a(n) = eulerphi(numdiv(n)); \\ Michel Marcus, Aug 22 2015

a(n) = A000010(A000005(n)). - Charles R Greathouse IV, Aug 11 2009

a(1) = 1, a(p) = 1 for p = primes (A000040), a(p*q) = 2 for p*q = product of two distinct primes (A006881), a(p*q*...*z) = 2^(k-1) for p*q*...*z = product of k (k > 2) distinct primes p, q, ..., z (A120944), a(p^(q-1)) = q - 1 for p, q = primes (A000040).

More terms from Carl Najafi, Aug 15 2011

Further extended by Antti Karttunen, Jul 23 2017

A163386 Primes p such that 4(p-4)-1 and 4(p-4)+1 are twin primes.

Original entry on oeis.org

5, 7, 19, 31, 61, 109, 211, 277, 367, 409, 421, 487, 571, 829, 967, 1009, 1069, 1201, 1237, 1279, 1471, 1579, 1669, 1699, 1741, 1831, 2161, 2521, 2539, 2719, 2797, 3067, 4021, 4051, 4177, 4261, 4327, 4441, 4519, 4567, 4639, 4789, 4861, 5197, 5407, 5527

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 25 2009

nonn

In other words, primes p such that 4*(p-4) is member of A014574. [Omar E. Pol, Aug 05 2009]

			4*(5-4)=4, 4*(7-4)=12, 4*(19-4)=60,...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A163385.

Cf. A014574, A163387, A163378. [Omar E. Pol, Aug 05 2009]

f1[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False]; f2[n_]:=If[f1[n]&&PrimeQ[n/4+4],True,False]; lst={};Do[If[f2[n],AppendTo[lst,n/4+4]],{n,8!}];lst
Select[Prime[Range[3,750]],And@@PrimeQ[4(#-4)+{1,-1}]&] (* Harvey P. Dale, Jan 24 2014 *)

Edited by Omar E. Pol, Aug 06 2009

cp's OEIS Frontend

A163109 a(n) = phi(tau(n)).

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