A371185 Indices of the cubefull numbers in the sequence of powerful numbers.

1, 3, 5, 7, 8, 11, 13, 17, 18, 23, 25, 26, 30, 34, 38, 41, 42, 45, 49, 54, 55, 61, 63, 72, 77, 78, 80, 82, 83, 87, 89, 93, 99, 105, 106, 113, 115, 116, 127, 128, 130, 137, 140, 148, 151, 153, 161, 164, 166, 179, 185, 186, 188, 192, 196, 201, 206, 221, 227, 234

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to powerful numbers.

Formula

A001694(a(n)) = A036966(n).

a(n) ~ c * n^(3/2), where c = A090699 / A362974^(3/2) = 0.216089803749...

Example

The first 5 powerful numbers are 1, 4, 8, 9, and 16. The 1st, 3rd, and 5th, 1, 8, and 16, are also cubefull numbers. Therefore, the first 3 terms of this sequence are 1, 3, and 5.

Mathematica

powQ[n_, emin_] := n == 1 || AllTrue[FactorInteger[n], Last[#] >= emin &]; Position[Select[Range[20000], powQ[#, 2] &], _?(powQ[#1, 3] &), Heads -> False] // Flatten

Prog

(PARI) ispow(n, emin) = n == 1 || vecmin(factor(n)[, 2]) >= emin;
lista(kmax) = {my(f, c = 0); for(k = 1, kmax, if(ispow(k, 2), c++; if(ispow(k, 3), print1(c, ", ")))); }

Crossrefs

Cf. A001694, A036966.

Cf. A090699, A362974.

Similar sequences: A361936, A371186.

Sequence in context: A047485 A024969 A296233 * A276112 A228075 A309405

Adjacent sequences: A371182 A371183 A371184 * A371186 A371187 A371188

Keyword

nonn,easy

Author

Amiram Eldar, Mar 14 2024

Status

approved