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A102218 2-Monica numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

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.

LINKS

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A007953, A018252, A102216, A102219, A118503, A177927.

Sequence in context: A310976 A155878 A029886 * A257586 A172458 A175226

Adjacent sequences:  A102215 A102216 A102217 * A102219 A102220 A102221

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein, Dec 30 2004

STATUS

approved

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Last modified May 28 07:06 EDT 2022. Contains 354112 sequences. (Running on oeis4.)