A147549 a(n) is the number of n-digit numbers m such that phi(m)=phi(10^n+1), gcd(10^n+1,m)=1 and 10 doesn't divide m.

0, 0, 3, 1, 3, 4, 11, 17, 116, 25, 222, 1806, 54, 223, 302422, 213, 35, 320146, 8, 1403

Offset

1,3

Comments

If 10^n+1 is prime (n must be of the form 2^k) then a(n)=0 because in this case there is no n-digit number m such that phi(10^n+1) = 10^n = phi(m). I defined this sequence and sequences A147547 and A147548 to answer a question (Nov 06 2008) from M. F. Hasler about the infiniteness of the "primitive" elements (those that aren't multiples of 10) of sequence A147619.

Links

Table of n, a(n) for n=1..20.

Mathematica

a[n_]:=(b=10^n+1; c=EulerPhi[b]; e=b-2; If[PrimeQ[b], 0, Length[Select[Range[ c+1, e], Mod[ #, 10]>0 && GCD[ #, b]==1 && EulerPhi[b]==EulerPhi[ # ]&]]]); Do[Print[a[n]], {n, 9}]

Crossrefs

Cf. A147547, A147548.

Sequence in context: A175186 A021323 A284619 * A177355 A349819 A076157

Adjacent sequences: A147546 A147547 A147548 * A147550 A147551 A147552

Keyword

nonn,base,hard,more

Author

Farideh Firoozbakht, Nov 12 2008

Extensions

a(10)-a(14) from Max Alekseyev, Mar 12 2009

a(15)-a(20) from Hiroaki Yamanouchi, Aug 27 2014

Status

approved