A113620 Numbers whose 3 prime powers are a permutation of each other. Numbers with 3 distinct prime factors whose 3 exponents are a permutation of the 3 bases.

21600, 36000, 48600, 121500, 169344, 225000, 337500, 395136, 857304, 3000564, 6690816, 19600000, 24532992, 37380096, 53782400, 59295096, 88942644, 122500000, 161980416, 171478296, 658834400, 774400000, 943130628, 1022754816, 2155524696, 2344190625, 4326400000

Offset: 1

Author

Jonathan Vos Post, Jan 26 2006

Keywords

• easy
• nonn

Examples

			21600 = 2^5 * 3^3 * 5^2
36000 = 2^5 * 3^2 * 5^3
48600 = 2^3 * 3^5 * 5^2
121500 = 2^2 * 3^5 * 5^3
169344 = 2^7 * 3^3 * 7^2
225000 = 2^3 * 3^2 * 5^5
337500 = 2^2 * 3^3 * 5^5
395136 = 2^7 * 3^2 * 7^3
857304 = 2^3 * 3^7 * 7^2
3000564 = 2^2 * 3^7 * 7^3
6690816 = 2^11 * 3^3 * 11^2
24532992 = 2^11 * 3^2 * 11^3
37380096 = 2^13 * 3^3 * 13^2
59295096 = 2^3 * 3^2 * 7^7
88942644 = 2^2 * 3^3 * 7^7
161980416 = 2^13 * 3^2 * 13^3
171478296 = 2^3 * 3^11 * 11^2
943130628 = 2^2 * 3^11 * 11^3
2155524696 = 2^3 * 3^13 * 13^2
2344190625 = 3^7 * 5^5 * 7^3
4594613625 = 3^7 * 5^3 * 7^5
6511640625 = 3^5 * 5^7 * 7^3
14010910524 = 2^2 * 3^13 * 13^3
25015118625 = 3^5 * 5^3 * 7^7
35452265625 = 3^3 * 5^7 * 7^5
69486440625 = 3^3 * 5^5 * 7^7
736820803125 = 3^11 * 5^5 * 11^3
3083660425988 = 2^2 * 3^3 * 11^11
3566212687125 = 3^11 * 5^3 * 11^5
15792626953125 = 3^5 * 5^11 * 11^3
20542440283992 = 2^3 * 3^2 * 11^11
212323095703125 = 3^3 * 5^11 * 11^5
8666341994809125 = 3^5 * 5^3 * 11^11
21807007674642216 = 2^3 * 3^2 * 13^13
24073172207803125 = 3^3 * 5^5 * 11^11
32710511511963324 = 2^2 * 3^3 * 13^13
		

Crossrefs

Cf. A113855.

Formula

{a(n)} = {p(1)^a * p(2)^b * p(3)^c for 3 distinct primes p(1), p(2), p(3) such that (a, b, c) is a permutation of (p(1), p(2), p(3))}.

Extensions

a(10)-a(27) from Giovanni Resta, Jun 13 2016