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2-Monica numbers.
3

%I #13 Apr 23 2021 05:18:15

%S 4,8,10,12,14,15,22,26,27,35,42,44,45,54,56,58,60,62,63,64,65,68,78,

%T 84,85,88,90,92,94,96,99,102,108,111,118,119,121,122,123,126,129,133,

%U 136,138,141,143,145,152,155,158,159,160,161,164,165,166,169,174,175

%N 2-Monica numbers.

%C 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

%D József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384.

%D James J. Tattersall, Elementary Number Theory in Nine Chapters, 2nd ed., Cambridge University Press, 2005, p. 93.

%H Amiram Eldar, <a href="/A102218/b102218.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael Smith, <a href="https://www.fq.math.ca/Scanned/34-2/smith.pdf">Cousins of Smith Numbers: Monica and Suzanne Sets</a>, Fibonacci Quarterly, Vol. 34, No. 2 (1996), pp. 102-104.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MonicaSet.html">Monica Set</a>.

%t 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 *)

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

%K nonn,base

%O 1,1

%A _Eric W. Weisstein_, Dec 30 2004