This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046346 Composite numbers that are divisible by the sum of their prime factors (counted with multiplicity). 15
 4, 16, 27, 30, 60, 70, 72, 84, 105, 150, 180, 220, 231, 240, 256, 286, 288, 308, 378, 440, 450, 476, 528, 540, 560, 576, 588, 594, 624, 627, 646, 648, 650, 728, 800, 805, 840, 884, 897, 900, 945, 960, 1008, 1040, 1056, 1080, 1100, 1122, 1134, 1160, 1170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If m is in the sequence and d|m, then m^d is also a term. Note that this sequence contains all infinite subsequences of the form p^(p^k) for k>0, where p is a prime. - Amiram Eldar and Thomas Ordowski, Feb 06 2019 If one selects some composite k, k >= 8, and decomposes (k - sopfr(k)) into an additive partition having only prime parts, then those parts, when taken as a product with k, yield an element of this sequence. - Christopher Hohl, Jul 30 2019 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 K. Alladi and P. Erdős, On an additive arithmetic function, Pacific J. Math., Volume 71, Number 2 (1977), 275-294. See "special numbers" on page 287. EXAMPLE a(38)=884 ->= 2 * 2 * 13 * 17 -> 2 + 2 + 13 + 17 = 34 so 884 / 34 = 26. MAPLE isA046346 := proc(n)     if isprime(n) then         false;     elif modp(n, A001414(n)) = 0 then         true;     else         false;     end if; end proc: for n from 2 to 1000 do     if isA046346(n) then         printf("%d, ", n);     end if; end do: # R. J. Mathar, Jan 12 2016 MATHEMATICA Select[Range[2, 1170], !PrimeQ[#]&&IntegerQ[#/Total[Times@@@FactorInteger[#]]]&] (* Jayanta Basu, Jun 02 2013 *) PROG (PARI) sopfr(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]); } lista(nn) = forcomposite(n=2, nn, if (! (n % sopfr(n)), print1(n, ", ")); ); \\ Michel Marcus, Jan 06 2016 (MATLAB) m=1; for u=2:1200 if and(isprime(u)==0, mod(u, sum(factor(u)))==0); sol(m)=u; m=m+1; end; end; sol % Marius A. Burtea, Jul 31 2019 (MAGMA) [k:k in [2..1200]| not IsPrime(k) and  k mod (&+[m*m: m in Factorization(k)]) eq 0]; // Marius A. Burtea, Jul 31 2019 CROSSREFS Cf. A036844, A046347, A046348, A001414. Contains A071142. Sequence in context: A210002 A105078 A050707 * A134330 A097764 A227993 Adjacent sequences:  A046343 A046344 A046345 * A046347 A046348 A046349 KEYWORD nonn AUTHOR Patrick De Geest, Jun 15 1998 EXTENSIONS Description corrected by Robert A. Stump (bee_ess107(AT)yahoo.com), Jan 09 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)