A391501 a(n) is the number of composites k such that radical(k) = sopfr(k) = A350352(n).

11, 16, 26, 29, 31, 41, 46, 47, 46, 56, 56, 68, 74, 74, 71, 81, 76, 83, 88, 6489, 91, 101, 106, 107, 101, 116, 106, 120, 126, 116, 130, 131, 128, 137, 131, 146, 16465, 158, 146, 166, 151, 164, 173, 182, 23164, 186, 166, 185, 182, 194, 176, 202, 191, 198, 200, 181

Offset

1,1

Comments

a(n) is the number of composites k such that A007947(k) = A001414(k) = A350352(n).

Links

Felix Huber, Table of n, a(n) for n = 1..697

Example

The a(1) = 11 composites k such that radical(k) = sopfr(k) = A350352(1) = 30 are 2^1*3^1*5^5 = 18750, 2^2*3^2*5^4 = 22500, 2^6*3^1*5^3 = 24000, 2^3*3^3*5^3 = 27000, 2^7*3^2*5^2 = 28800, 2^11*3^1*5^1 = 30720, 2^4*3^4*5^2 = 32400, 2^8*3^3*5^1 = 34560, 2^1*3^6*5^2 = 36450, 2^5*3^5*5^1 = 38880 and 2^2*3^7*5^1 = 43740.

Maple

A391501 := proc(n) local m, f, p, r, c, i, s; m := A350352(n); f := ifactors(m)[2]; p := [seq(f[i][1], i = 1 .. nops(f))]; r := nops(p); c := 0; s := proc(i, n) local e; if i = r then if n mod p[r] = 0 and 1 <= n/p[r] then c := c + 1; end if; else for e to floor((n - r + i)/p[i]) do s(i + 1, n - p[i]*e); end do; end if; end proc; s(1, m); c; end proc: seq(A391501(n), n = 1 .. 56);

Crossrefs

Cf. A001414, A007947, A002808, A350352, A391316.

Sequence in context: A371187 A110031 A166451 * A109307 A327752 A128835

Adjacent sequences: A391498 A391499 A391500 * A391502 A391503 A391504

Keyword

nonn

Author

Felix Huber, Dec 23 2025

Status

approved