A363292 Numbers whose sum of (distinct) prime divisors (A008472) equals 7.

7, 10, 20, 40, 49, 50, 80, 100, 160, 200, 250, 320, 343, 400, 500, 640, 800, 1000, 1250, 1280, 1600, 2000, 2401, 2500, 2560, 3200, 4000, 5000, 5120, 6250, 6400, 8000, 10000, 10240, 12500, 12800, 16000, 16807, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960

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), A000420 (7^n), A033846 (2^m*5^n), A362948 (A008472 = 5).

Programs

Mathematica

seq[max_] := Union[Join[7^Range[Floor[Log[7, max]]], Flatten@ Table[2^i*5^j, {i, 1, Log2[max]}, {j, 1, Log[5, max/2^i]}]]]; seq[40000] (* Amiram Eldar, Jul 27 2023 *)

PARI

select( {is_A363292(n)=vecsum(factor(n,0)[,1])==7}, [1..13^4]) \\ alternatively: [n | n<-[1..13^4], A008472(n)==7]

Formula

Union of A000420 = {7^k ; k > 0} and A033846 = {2^j*5^k ; j, k > 0}.

Sum_{n>=1} 1/a(n) = 5/12. - Amiram Eldar, Jul 27 2023