A112720 Numbers m such that phi(m) = 1^d_1 + 2^d_2 + ... + k^d_k where d_1 d_2 ... d_k is the decimal expansion of m.

1, 2, 6883, 1132856, 11059812

Offset

1,2

Comments

There is no further term up to 7*10^7.

a(6) > 10^12. - Giovanni Resta, Apr 13 2017

This sequence is full because for k > 10 and 10^k <= m < 10^(k+1), phi(m) > 10^k/f(10^k) > Sum_{i=1..k+1} i^9 >= Sum_{i=1..k+1} i^d_i, where f(n) = exp(gamma)*log(log(n)) + 2.5/log(log(n)) is given in A057635. - Jinyuan Wang, Aug 02 2020

Links

Table of n, a(n) for n=1..5.

Example

phi(11059812) = 1^1 + 2^1 + 3^0 + 4^5 + 5^9 + 6^8 + 7^1 + 8^2 so 11059812 is in the sequence.

Mathematica

Do[d=IntegerDigits[n]; k=Length[d]; If[EulerPhi[n]==Sum[j^d[[j]], {j, k}], Print[n]], {n, 70000000}]

Crossrefs

Cf. A035138, A057635, A112718, A112719, A112721.

Sequence in context: A107022 A330901 A285693 * A129059 A129058 A129057

Adjacent sequences: A112717 A112718 A112719 * A112721 A112722 A112723

Keyword

nonn,base,fini,full

Author

Farideh Firoozbakht, Sep 17 2005

Status

approved