A354530 Numbers k such that k^2 is a minimal number; numbers k whose square is in A007416.

1, 2, 4, 6, 8, 12, 24, 30, 32, 36, 60, 64, 72, 96, 120, 180, 192, 210, 216, 256, 288, 360, 420, 480, 512, 576, 768, 840, 864, 900, 960, 1080, 1260, 1440, 1536, 1680, 1728, 1800, 2048, 2304, 2520, 2880, 3360, 3840, 4320, 4608, 4620, 5400, 6144, 6300, 6720, 6912, 7200, 7560

Offset

1,2

Comments

Numbers k such that there is no m < k^2 such that d(m) = d(k^2), d = A000005. Since only squares have an odd number of divisors, also numbers k such that there is no m < k such that d(m^2) = d(k^2).

Links

David A. Corneth, Table of n, a(n) for n = 1..14008 (first 310 terms from Jianing Song, terms <= 10^20).

Formula

d(a(n)^2) = A166722(n).

Example

8 is a term since 8^2 = 64 has 7 divisors and no smaller number (smaller square) has that many divisors.

Prog

(PARI) lista(nn) = {v = []; for (n=1, nn, d = numdiv(n^2); if (! vecsearch(v, d), print1(n, ", "); v = Set(concat(v, d))); ); } \\ from Michel Marcus's program for A166721

Crossrefs

Cf. A007416, A000005, A025487.

Square root of A166721. Also A016017 or A071571 sorted.

Cf. also A166722.

Sequence in context: A228515 A363145 A164145 * A140999 A168267 A308912

Adjacent sequences: A354527 A354528 A354529 * A354531 A354532 A354533

Keyword

nonn,easy

Author

Jianing Song, Aug 16 2022

Status

approved