This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177927 #31 Feb 16 2025 08:33:12 %S A177927 4,9,10,22,24,25,27,34,42,46,55,58,60,72,78,81,82,85,94,105,106,114, %T A177927 115,118,121,126,128,132,142,145,150,166,178,180,186,187,192,195,202, %U A177927 204,205,214,216,222,224,226,231,234,235,243,253,256,258,262,265,274,276,285,289,295 %N A177927 3-Monica numbers. %C A177927 3-Monica numbers are composite positive integers k for which 3 divides S(k)-Sp(k), where S(k) denotes the sum of the digits of k and Sp(k) denotes the sum of the digits in an extended prime factorization of k. %D A177927 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384. %D A177927 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 2005, page 93. %D A177927 E. W. Weisstein, The CRC Concise Encyclopedia of Mathematics, CRC Press, 1999, pages 1192-1193. %H A177927 Amiram Eldar, <a href="/A177927/b177927.txt">Table of n, a(n) for n = 1..10000</a> %H A177927 Michael Smith, <a href="https://web.archive.org/web/2024*/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 A177927 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MonicaSet.html">Monica Set</a>. %e A177927 S(10)=1+0=1, 10=2*5, Sp(10)=2+5=7, S(10)-Sp(10)=-6 which is divisible by 3. %t A177927 s[n_] := Plus @@ IntegerDigits[n]; f[p_, e_] := e*s[p]; sp[n_] := Plus @@ f @@@ FactorInteger[n]; mon3Q[n_] := CompositeQ[n] && Divisible[s[n] - sp[n], 3]; Select[Range[300], mon3Q] (* _Amiram Eldar_, Apr 23 2021 *) %Y A177927 Cf. A006753 (Smith numbers are a subset of every n-Monica sequence). %Y A177927 Cf. A102217 (n-Suzanne numbers are a subset of n-Monica numbers). %Y A177927 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)). %Y A177927 Cf. A007953, A118503. %K A177927 nonn,base %O A177927 1,1 %A A177927 _Chris Fry_, Dec 26 2010