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

1,1

Comments

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

Links

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

Example

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

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;

Prog

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

Crossrefs

Cf. A075657, A076380 - A076387.

Sequence in context: A036959 A108031 A280429 * A193622 A265249 A133451

Adjacent sequences: A076384 A076385 A076386 * A076388 A076389 A076390

Keyword

nonn,base

Author

Floor van Lamoen, Oct 08 2002

Status

approved