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A177927
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3-Monica numbers.
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1
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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
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1,1
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COMMENTS
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3-Monica 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.
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REFERENCES
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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 1192-1193.
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LINKS
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Table of n, a(n) for n=1..60.
Eric Weisstein's World of Mathematics, Monica Set
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EXAMPLE
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S(10)=1+0=1, 10=2*5, Sp(10)=2+5=7, S(10)-Sp(10)=-6 which is divisible by 3.
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CROSSREFS
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Cf. A006753. Smith numbers are a subset of every n-Monica sequence.
Cf. A102217. n-Suzanne numbers are a subset of n-Monica numbers.
Cf. A102219. This list of '3-Monica' 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
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KEYWORD
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nonn,base
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AUTHOR
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Chris Fry, Dec 26 2010
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STATUS
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approved
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