

A092320


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


1



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
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OFFSET

1,1


COMMENTS

Cal Q. Leytor (obviously an alias) asked for the lowest pair of consecutive wordfactorable numbers.
Lowest pair of consecutive wordfactorable numbers is 405406; next is 665666.  Ray Chandler, Feb 16 2004
Subsequence of A002808 (composite numbers).  Ivan N. Ianakiev, Mar 01 2020


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


EXAMPLE

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


MATHEMATICA

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


PROG

(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


CROSSREFS

Sequence in context: A344995 A115076 A126259 * A056495 A351523 A263656
Adjacent sequences: A092317 A092318 A092319 * A092321 A092322 A092323


KEYWORD

easy,nonn,word


AUTHOR

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


EXTENSIONS

More terms from Ray Chandler, Feb 16 2004


STATUS

approved



