A394753 Number of k <= m such that rad(k) | m, where rad = A007947 and m = A055932(n).

1, 2, 3, 5, 4, 8, 5, 10, 11, 18, 6, 14, 15, 16, 26, 7, 18, 32, 20, 21, 36, 8, 23, 41, 24, 44, 25, 68, 26, 49, 9, 53, 29, 55, 30, 58, 31, 96, 32, 64, 65, 33, 10, 69, 35, 71, 115, 36, 76, 78, 38, 81, 131, 39, 83, 84, 40, 11, 145, 88, 42, 91, 156, 43, 96, 97, 44

Offset

1,2

Comments

Analogous to A364225, which instead regards A025487, a proper subset of A055932.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14, with a color function showing primes in red, proper prime powers in gold, composite primorials in green, numbers neither squarefree nor powerful in blue, and powerful numbers that are not prime powers in purple.

Formula

a(n) = A010846(A055932(n)).

Length of row A055932(n) of A162306.

For numbers k in A055932 such that omega(k) = 1 (i.e., 2^m), a(k) = m, where omega = A001221.

For numbers k in A055932 such that omega(k) = 2 (i.e., k = A003586(i), 3-smooth k), a(k) = i.

For numbers k in A055932 such that omega(k) = 3 (i.e., k = A051037(j), 5-smooth k), a(k) = j, etc.

Mathematica

fQ[x_] := Or[IntegerQ[Log2[x]], And[EvenQ[x], Union[Differences[PrimePi[FactorInteger[x][[All, 1]] ] ] ] == {1}]]; a010846[x_] := Count[Range[x], _?(Divisible[x, Times @@ FactorInteger[#][[All, 1]] ] &) ]; Map[a010846, Select[Range[1600], fQ] ]
(* Alternative: load "theta" program from link at A369609, and function f from link at A376690 *)
Map[theta, Union@ Flatten@ f[6] ]

Crossrefs

Cf. A000010, A000079, A002110, A002473, A003586, A007947, A010846, A051037, A055932, A162306, A364225.

Sequence in context: A083464 A347423 A255234 * A364225 A256995 A249129

Adjacent sequences: A394750 A394751 A394752 * A394754 A394755 A394756

Keyword

nonn

Author

Michael De Vlieger, May 06 2026

Status

approved