A276513 a(n) = the smallest number k>1 such that Sum_{p|k} 0.p = n where p runs through the prime divisors of k.

21, 16102, 281785, 275867515, 9178864590, 8533159052845, 9404411107962990

Offset: 1

Author

Jaroslav Krizek, Sep 14 2016

Keywords

• nonn
• base
• more

Comments

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

a(n) = the smallest number k>1 such that A276651(k) / A276652(k) = n.

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, ...

Conjecture: a(4) = 730610790; Sum_{p|730610790} 0.p = 0.2 + 0.3 + 0.5 + 0.7 + 0.13 + 0.31 + 0.89 + 0.97 = 4.

Subsequence of A005117. - Chai Wah Wu, Sep 15 2016

a(8) <= 8646420251472669505, a(9) <= 1879755659507289195345, a(10) <= 3625424828481802325595910. - Giovanni Resta, Aug 19 2019

a(11) <= 771700218558425481527617170, a(12) <= 3840490537418012461017296489710. - Chai Wah Wu, Feb 07 2022

Examples

			Number 16102 is the smallest number k with Sum_{p|k} 0.p = 2; set of prime divisors of 16102: {2, 83, 97}; Sum_{p|16102} 0.p = 0.2 + 0.83 + 0.97 = 2.
		

Crossrefs

Cf. A005117, A276651, A276652, A276653, A276654, A276655.

Programs

Magma

A276513:=func; [A276513(n): n in[1..3]]

Mathematica

Table[k = 1;
While[f = FactorInteger[k][[All, 1]];
  Total[f*10^-IntegerLength[f]] != n, k++];
k, {n, 1, 4}] (* Robert Price, Sep 20 2019 *)

Extensions

a(4) from Chai Wah Wu, Sep 16 2016

a(5)-a(7) from Giovanni Resta, Aug 19 2019