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

1,1

Links

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A127306 A319184 A231959 * A168145 A276407 A022310

Adjacent sequences: A362945 A362946 A362947 * A362949 A362950 A362951

Keyword

nonn,easy

Author

M. F. Hasler, Jul 20 2023

Status

approved