login
Numbers n such that pi(n) = sigma(d_1)*sigma(d_2)*...*sigma(d_k) where d_1 d_2 ... d_k is the decimal expansion of n.
5

%I #18 Mar 05 2019 18:17:56

%S 15,155,252,916,1189,12654,55293,177554,418634,753248,885193,18252678,

%T 18252687,18469156,18469165,19882616,19882623,41867246,73526936,

%U 73526957,233843449,244895519,2345784285,2399877831,4273447776,29891923496,42649454852,728781494646

%N Numbers n such that pi(n) = sigma(d_1)*sigma(d_2)*...*sigma(d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

%C a(n) must necessarily be a zeroless number. - _Chai Wah Wu_, Mar 04 2019

%H Chai Wah Wu, <a href="/A098685/b098685.txt">Table of n, a(n) for n = 1..34</a>

%e 885193 is in the sequence because pi(885193) = sigma(8)*sigma(8)*sigma(5)*sigma(1)*sigma(9)*sigma(3).

%t Do[d=IntegerDigits[n];k=Length[d];If[ !MemberQ[d, 0]&&PrimePi[n]== Product[DivisorSigma[1, d[[j]]], {j, k}], Print[n]], {n, 10000000}]

%Y Cf. A000203, A000720, A052382, A098686, A098683, A098684.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Sep 24 2004

%E a(12)-a(25) from _Donovan Johnson_, Jun 18 2009

%E a(26)-a(28) from _Chai Wah Wu_, Mar 04 2019