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A076387
Numbers n such that sum of digits in base 9 is a divisor of sum of prime divisors (A008472).
8
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
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
KEYWORD
nonn,base
AUTHOR
Floor van Lamoen, Oct 08 2002
STATUS
approved