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A046346 Composite numbers that are divisible by the sum of their prime factors (counted with multiplicity). 13
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

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

CROSSREFS

Cf. A036844, A046347, A046348, A001414.

Sequence in context: A105078 A050707 * A134330 A097764 A227993 A072873

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 July 22 03:22 EDT 2017. Contains 289648 sequences.