A076387 Numbers n such that sum of digits in base 9 is a divisor of sum of prime divisors (A008472).

2, 3, 5, 7, 9, 21, 27, 65, 69, 70, 81, 84, 90, 110, 123, 126, 130, 133, 154, 189, 222, 228, 243, 252, 259, 264, 327, 329, 333, 340, 342, 343, 350, 365, 372, 381, 402, 434, 450, 516, 528, 580, 588, 618, 621, 650, 684, 729, 730, 731, 738, 740, 741, 756, 765, 774

Offset: 1

Author

Floor van Lamoen, Oct 08 2002

Keywords

• nonn
• base

Comments

The sequence is infinite because, for m = 9^k, k >= 0, digsum(m_9) = 1. - Marius A. Burtea, Jul 10 2019

Examples

			21 = 23_9, digsum(23_9) = 5, PrimeDivisors(21) = {3, 7}, sopf(21) = 3+7 = 10 = 5*2.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..5189

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

Magma

[n: n in [1..800]| &+PrimeDivisors(n) mod &+Intseq(n,9) eq 0] ; // Marius A. Burtea, Jul 10 2019

Maple

A076387 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 9); t1 := floor(t1/9); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;

PARI

{for(ixp=2,783,
casi=ixp;cvst=0;dsu=0;M=factor(ixp);smt=0;
for(i=1,matsize(M)[1],smt=smt+M[i, 1]);
while(casi!=0,
cvd=casi%9;dsu=dsu+cvd;casi=(casi-cvd)/9);
if(smt%dsu==0,print1(ixp,", ")))} \\ Douglas Latimer, May 08 2012