%I
%S 2,3,4,5,7,11,13,16,17,19,23,27,29,30,31,37,41,43,47,53,59,60,61,67,
%T 70,71,72,73,79,83,84,89,97,101,103,105,107,109,113,127,131,137,139,
%U 149,150,151,157,163,167,173,179,180,181,191,193,197,199,211,220,223
%N Numbers n such that n / sopfr(n) is an integer, where sopfr = sumofprimefactors, A001414.
%C Union of A046346 and the primes.  _T. D. Noe_, Feb 20 2007
%C A238525(a(n)) = 0.  _Reinhard Zumkeller_, Jul 21 2014
%C These are the Heinz numbers of the partitions counted by A330953.  _Gus Wiseman_, Jan 17 2020
%D Amarnath Murthy, Generalization of Partition function and introducing Smarandache Factor Partition, Smarandache Notions Journal, Vol. 11, 123, Spring2000.
%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 89.
%H T. D. Noe, <a href="/A036844/b036844.txt">Table of n, a(n) for n = 1..1000</a>
%H K. Alladi and P. ErdÅ‘s, <a href="http://projecteuclid.org/euclid.pjm/1102811427">On an additive arithmetic function</a>, Pacific J. Math., Volume 71, Number 2 (1977), 275294.
%H M. Lal, <a href="http://dx.doi.org/10.1090/S00255718196902427659">Iterates of a numbertheoretic function</a>, Math. Comp., 23 (1969), 181183.
%e a(12) = 27 because sopfr(27) = 3 + 3 + 3 = 9 and 27 is divisible by 9.
%t Select[Range[2, 224], Divisible[#, Plus @@ Times @@@ FactorInteger[#]] &] (* _Jayanta Basu_, Aug 13 2013 *)
%o (PARI) is_A036844(n)=n>1 && !(n%A001414(n)) \\ _M. F. Hasler_, Mar 01 2014
%o (Haskell)
%o a036844 n = a036844_list !! (n1)
%o a036844_list = filter ((== 0). a238525) [2..]
%o  _Reinhard Zumkeller_, Jul 21 2014
%Y sopfr(n) is defined in A001414.
%Y The version for prime indices instead of prime factors is A324851.
%Y Partitions whose Heinz number is divisible by their sum: A330950.
%Y Partitions whose Heinz number is divisible by their sum of primes: A330953.
%Y Partitions whose product is divisible by their sum of primes: A330954.
%Y Partitions whose product divides their sum of primes: A331381.
%Y Product of prime indices is divisible by sum of prime factors: A331378.
%Y Sum of prime factors is divisible by sum of prime indices: A331380.
%Y Product of prime indices equals sum of prime factors: A331384.
%Y Cf. A056239, A112798, A120383, A238525, A331379, A331382, A331383.
%K nonn
%O 1,1
%A Robert A. Stump (bee_ess107(AT)yahoo.com), Jan 09 2002
