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

Author

Jianing Song, Aug 16 2022

Keywords

• nonn
• easy

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).

Examples

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

Links

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

Crossrefs

Cf. A007416, A000005, A025487.

Square root of A166721. Also A016017 or A071571 sorted.

Cf. also A166722.

Programs

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

Formula

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