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

1,1

Links

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A064210 A249942 A300021 * A327977 A097634 A120312

Adjacent sequences: A363289 A363290 A363291 * A363293 A363294 A363295

Keyword

nonn,easy

Author

M. F. Hasler, Jul 20 2023

Status

approved