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A102218
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2-Monica numbers.
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3
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4, 8, 10, 12, 14, 15, 22, 26, 27, 35, 42, 44, 45, 54, 56, 58, 60, 62, 63, 64, 65, 68, 78, 84, 85, 88, 90, 92, 94, 96, 99, 102, 108, 111, 118, 119, 121, 122, 123, 126, 129, 133, 136, 138, 141, 143, 145, 152, 155, 158, 159, 160, 161, 164, 165, 166, 169, 174, 175
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OFFSET
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1,1
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COMMENTS
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Composite numbers k such that the difference between the sum of digits of k (A007953) and the sum of sums of digits of the prime factors of k (taken with multiplicity, A118503) is even. - Amiram Eldar, Apr 23 2021
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REFERENCES
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József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384.
James J. Tattersall, Elementary Number Theory in Nine Chapters, 2nd ed., Cambridge University Press, 2005, p. 93.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
Michael Smith, Cousins of Smith Numbers: Monica and Suzanne Sets, Fibonacci Quarterly, Vol. 34, No. 2 (1996), pp. 102-104.
Eric Weisstein's World of Mathematics, Monica Set.
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MATHEMATICA
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s[n_] := Plus @@ IntegerDigits[n]; f[p_, e_] := e*s[p]; sp[n_] := Plus @@ f @@@ FactorInteger[n]; mon2Q[n_] := CompositeQ[n] && EvenQ[s[n] - sp[n]]; Select[Range[200], mon2Q] (* Amiram Eldar, Apr 23 2021 *)
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CROSSREFS
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Cf. A007953, A018252, A102216, A102219, A118503, A177927.
Sequence in context: A310976 A155878 A029886 * A257586 A172458 A175226
Adjacent sequences: A102215 A102216 A102217 * A102219 A102220 A102221
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KEYWORD
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nonn,base
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AUTHOR
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Eric W. Weisstein, Dec 30 2004
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STATUS
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approved
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