A135101 - OEIS

%I #18 Jan 14 2024 12:30:40

%S 1,2,3,10,15,24,55,46,71,116,101,180,213,196,205,276,307,444,337,610,

%T 621,646,687,808,985,876,921,996,1049,1184,1417,1576,1665,1576,2127,

%U 1836,2377,1660,2201,2088,2731,2844,2847,2944,3317,3232,3503,3294,3165

%N Digital sum (base the n-th prime) of n^n.

%H G. C. Greubel, <a href="/A135101/b135101.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ds_prime(n)(n^n), where ds_prime(n) = digital sum base the n-th prime.

%F a(n) = n^n - (prime(n)-1)*Sum{k>0} ( floor(n^n/prime(n)^k) ).

%e a(2) = ds_prime(2)(2^2) = ds_3(4) = 1+1 = 2;

%e a(10) = ds_prime(5)(5^5) = ds_11(3125) = 2+3+9+1 = 15.

%t Table[Total[IntegerDigits[n^n, Prime[n]]], {n, 50}] (* _G. C. Greubel_, Sep 23 2016 *)

%o (PARI) a(n) = vecsum(digits(n^n, prime(n))); \\ _Michel Marcus_, Sep 24 2016

%Y Cf. A000040, A000045, A007953, A054899, A075771, A131451, A133620, A133900, A134599.

%K nonn,base

%O 1,2

%A _Hieronymus Fischer_, Dec 24 2007