A092320 "Word-factorable" numbers, or numbers k that are divisible by the number of letters in the American English word(s) for k.

4, 6, 12, 30, 33, 36, 40, 45, 50, 54, 56, 60, 70, 81, 88, 90, 100, 112, 150, 162, 170, 200, 240, 252, 300, 304, 336, 340, 405, 406, 418, 456, 513, 525, 528, 551, 560, 567, 600, 660, 665, 666, 693, 704, 720, 748, 810, 828, 850, 858, 874, 882, 897, 910, 924, 960, 1005

Offset: 1

Author

Bryce Herdt (mathidentity(AT)aol.com), Feb 15 2004

Keywords

• easy
• nonn
• word

Comments

Cal Q. Leytor (obviously an alias) asked for the lowest pair of consecutive word-factorable numbers.

Lowest pair of consecutive word-factorable numbers is 405-406; next is 665-666. - Ray Chandler, Feb 16 2004

Subsequence of A002808 (composite numbers). - Ivan N. Ianakiev, Mar 01 2020

Examples

			"One hundred twelve" has 16 letters and 112=16*7, so 112 is a term.
		

References

• Cal Q. Leytor, The Word Factor, GAMES, October 1986, page 52.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Range[1000],Divisible[#,StringLength[StringReplace[IntegerName[#],
{"\[Hyphen]" -> "", " " -> ""}]]] &] (* Ivan N. Ianakiev, Mar 01 2020 *)

Python

from num2words import num2words as n2w
def letters(n): return sum(c.isalpha() for c in n2w(n).replace(" and", ""))
def ok(n): return n%letters(n) == 0
print([k for k in range(1, 1000) if ok(k)]) # Michael S. Branicky, Jan 17 2022

Extensions

More terms from Ray Chandler, Feb 16 2004