A276654 - OEIS

%I #29 Sep 08 2022 08:46:17

%S 2,21,2905,281785,47740490,9178864590,8533159052845,1817562878255985,

%T 1801204812351681135,787408225243814333670

%N a(n) = the smallest number k>1 such that floor(Sum_{p|k} 0.p) = n where p runs through the prime divisors of k.

%C Here 0.p means the decimal fraction obtained by writing p after the decimal point, e.g. 0.11 = 11/100.

%C The first few values of Sum_{p|n} 0.p are: 1/5, 3/10, 1/5, 1/2, 1/2, 7/10, 1/5, 3/10, 7/10, ...

%C Subsequence of A005117. - _Chai Wah Wu_, Sep 15 2016

%e Number 2905 is the smallest number k with floor(Sum_{p|k} 0.p) = 2; set of prime divisors of 2905: {5, 7, 83}; floor(Sum_{p|2905} 0.p) = 0.5 + 0.7 + 0.83 = floor(2.03) = 2.

%t Table[k = 2; While[f = FactorInteger[k][[All, 1]];

%t   Floor[Total[f*10^-IntegerLength[f]]] != n, k++];

%t k, {n, 0, 3}] (* _Robert Price_, Sep 20 2019 *)

%o (Magma) A276654:=func<n|exists(r){k:k in[2..1000000] | Floor(&+[d / (10^(#Intseq(d))): d in PrimeDivisors(k)]) eq n}select r else 0>; [A276654(n): n in[0..3]]

%Y Cf. A005117, A276513, A276651, A276652, A276653, A276655.

%K nonn,base,more

%O 0,1

%A _Jaroslav Krizek_, Sep 11 2016

%E a(4) from _Michel Marcus_, Sep 11 2016

%E a(5)-a(9) from _Giovanni Resta_, Aug 31 2019