A289142 Numbers such that the sum of prime factors (taken with multiplicity) is divisible by 3.

1, 3, 8, 9, 14, 20, 24, 26, 27, 35, 38, 42, 44, 50, 60, 62, 64, 65, 68, 72, 74, 77, 78, 81, 86, 92, 95, 105, 110, 112, 114, 116, 119, 122, 125, 126, 132, 134, 143, 146, 150, 155, 158, 160, 161, 164, 170, 180, 185, 186, 188, 192, 194, 195, 196, 203, 204

Offset

1,2

Comments

U{S(n); 3|n}, where S(n)= {x; sopfr(x)=n}; numbers placed in ascending order.

A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - Robert Israel, Jul 03 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

sopfr(42)=2+3+7=12=4*3, sopfr(95)=5+19=23=8*3, sopfr(180)=2+2+3+3+5=15=5*3.

Maple

select(n -> add(t[1]*t[2], t=ifactors(n)[2]) mod 3 = 0, [$1..1000]); # Robert Israel, Jul 03 2017

Mathematica

Select[Range@ 243, Divisible[Total@ Flatten[Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#]]], 3] &] (* Michael De Vlieger, Jun 28 2017 *)
oin[{1}, Select[Range[250], Mod[Total[Times@@@FactorInteger[#]], 3]==0&]] (* Harvey P. Dale, Mar 16 2020 *)

Prog

(PARI) s(n)=my(f=factor(n), p=f[, 1], e=f[, 2]); sum(k=1, #p, e[k]*p[k]);
for(n=1, 200, if(s(n)%3==0, print1(n, ", "))); \\ Joerg Arndt, Jun 26 2017

Crossrefs

Cf. A001414 (sopfr), A036349, A036350, A046363.

Sequence in context: A084747 A286177 A287579 * A101065 A152411 A080517

Adjacent sequences: A289139 A289140 A289141 * A289143 A289144 A289145

Keyword

nonn

Author

David James Sycamore, Jun 26 2017

Extensions

Corrected by Robert Israel, Jul 03 2017

Status

approved