A362948 Numbers whose sum of (distinct) prime divisors (A008472) equals 5.

5, 6, 12, 18, 24, 25, 36, 48, 54, 72, 96, 108, 125, 144, 162, 192, 216, 288, 324, 384, 432, 486, 576, 625, 648, 768, 864, 972, 1152, 1296, 1458, 1536, 1728, 1944, 2304, 2592, 2916, 3072, 3125, 3456, 3888, 4374, 4608, 5184, 5832, 6144, 6912, 7776, 8748, 9216, 10368, 11664, 12288

Offset: 1

Author

M. F. Hasler, Jul 20 2023

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008472 (sopf), A000351 (5^n), A033845 (2^m*3^n).

Programs

Mathematica

seq[max_] := Union[Join[5^Range[Floor[Log[5, max]]], Flatten@ Table[2^i*3^j, {i, 1, Log2[max]}, {j, 1, Log[3, max/2^i]}]]]; seq[13000] (* Amiram Eldar, Jul 27 2023 *)

PARI

select( {is_A362948(n)=vecsum(factor(n,0)[,1])==5}, [1..11^4]) \\ alternatively: [n | n<-[1..11^4], A008472(n)==5]

Formula

Union of A000351 = {5^k ; k > 0} and A033845 = {2^j*3^k, j,k > 0}.

Sum_{n>=1} 1/a(n) = 3/4. - Amiram Eldar, Jul 27 2023