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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[1]*m[2]: 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

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