

A177927


3Monica numbers.


1



4, 9, 10, 22, 24, 25, 27, 34, 42, 46, 55, 58, 60, 72, 78, 81, 82, 85, 94, 105, 106, 114, 115, 118, 121, 126, 128, 132, 142, 145, 150, 166, 178, 180, 186, 187, 192, 195, 202, 204, 205, 214, 216, 222, 224, 226, 231, 234, 235, 243, 253, 256, 258, 262, 265, 274, 276, 285, 289, 295
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OFFSET

1,1


COMMENTS

3Monica numbers are composite positive integers n for which 3 divides S(n)Sp(n), where S(n) denotes the sum of the digits of n and Sp(n) denotes the sum of the digits in an extended prime factorization of n.


REFERENCES

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 2005, page 93.
E. W. Weisstein, The CRC Concise Encyclopedia of Mathematics, CRC Press, 1999, pages 11921193.


LINKS

Table of n, a(n) for n=1..60.
Eric Weisstein's World of Mathematics, Monica Set


EXAMPLE

S(10)=1+0=1, 10=2*5, Sp(10)=2+5=7, S(10)Sp(10)=6 which is divisible by 3.


CROSSREFS

Cf. A006753. Smith numbers are a subset of every nMonica sequence.
Cf. A102217. nSuzanne numbers are a subset of nMonica numbers.
Cf. A102219. This list of '3Monica' numbers is incorrect. It does not contain all the Smith numbers and appears to be based on S(n)+Sp(n)=0(mod 3), instead of S(n)Sp(n)=0(mod 3).
Sequence in context: A109412 A061766 A109448 * A062398 A030754 A244863
Adjacent sequences: A177924 A177925 A177926 * A177928 A177929 A177930


KEYWORD

nonn,base


AUTHOR

Chris Fry, Dec 26 2010


STATUS

approved



