A375240 For squarefree j, a(j*k^2) = j * a(k), a(1) = 1.

1, 2, 3, 2, 5, 6, 7, 4, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 12, 5, 26, 9, 14, 29, 30, 31, 4, 33, 34, 35, 6, 37, 38, 39, 20, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 18, 55, 28, 57, 58, 59, 30, 61, 62, 21, 4, 65, 66, 67, 34, 69

Offset

1,2

Links

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

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.

Formula

Multiplicative with a(p^e) = p^A000120(e).

a(n) = A007913(n) * a(A000188(n)).

a(n) = Product_{k >= 0} A007947(A352780(n,k)). - Peter Munn, Aug 23 2024

Mathematica

Array[Apply[Times, FactorInteger[#] /. {p_Integer, e_Integer} :> p^DigitCount[e, 2, 1]] &, 69] (* Michael De Vlieger, Aug 07 2024 *)

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^hammingweight(f[i, 2])); } \\ Amiram Eldar, Jan 13 2026

Crossrefs

Cf. A000120, A000188, A007913, A007947, A352780.

Sequence in context: A382888 A277803 A062789 * A066069 A019530 A355263

Adjacent sequences: A375237 A375238 A375239 * A375241 A375242 A375243

Keyword

nonn,easy,mult

Author

Peter Munn, Aug 07 2024

Status

approved