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A074037 Sum of the composites between the smallest prime factor of n and the largest prime factor of n.

%I A074037 #20 Aug 14 2020 07:58:41
%S A074037 0,0,0,0,0,0,0,0,0,4,0,0,0,10,4,0,0,0,0,4,10,37,0,0,0,49,0,10,0,4,0,0,
%T A074037 37,94,6,0,0,112,49,4,0,10,0,37,4,175,0,0,0,4,94,49,0,0,33,10,112,305,
%U A074037 0,4,0,335,10,0,45,37,0,94,175,10,0,0,0,505,4,112,27,49,0,4,0,622,0,10
%N A074037 Sum of the composites between the smallest prime factor of n and the largest prime factor of n.
%C A074037 Record values (A079725) occur at 2*primes (A001747).
%H A074037 Harvey P. Dale, <a href="/A074037/b074037.txt">Table of n, a(n) for n = 1..1000</a>
%H A074037 Jason Earls, <a href="https://pdfs.semanticscholar.org/301f/777cd44aaa90b1a24c2ddc1d07721bbc9051.pdf">Some Smarandache-type sequences and problems concerning abundant and deficient numbers</a>, in Smarandache Notions Journal (2004), Vol. 14.1, pp 265-270.
%e A074037 a(14) = 10 because 2*7 = 14 and 4 + 6 = 10.
%p A074037 with(numtheory): a:=proc(n) local nf,nnf,s,j: nf:=factorset(n): nnf:=nops(nf): s:=0: for j from nf[1] to nf[nnf] do if isprime(j)=false then s:=s+j else s:=s: fi: od: s: end: 0,seq(a(n),n=2..84); # _Emeric Deutsch_
%t A074037 sc[n_]:=Module[{pfacs=Transpose[FactorInteger[n]][[1]],a,b}, a=Min[ pfacs]+1; b=Max[pfacs]-1;Total[Select[Range[a,b],!PrimeQ[#]&]]]; Array[sc,90] (* _Harvey P. Dale_, Nov 14 2011 *)
%K A074037 easy,nonn
%O A074037 1,10
%A A074037 _Jason Earls_, Sep 15 2002