A102218 2-Monica numbers.

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

Offset: 1

Author

Eric W. Weisstein, Dec 30 2004

Keywords

• nonn
• base

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.

Crossrefs

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

Programs

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 *)