A074037 - OEIS

%I #20 Aug 14 2020 07:58:41

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

%C Record values (A079725) occur at 2*primes (A001747).

%H Harvey P. Dale, <a href="/A074037/b074037.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 a(14) = 10 because 2*7 = 14 and 4 + 6 = 10.

%p 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 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 easy,nonn

%O 1,10

%A _Jason Earls_, Sep 15 2002