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

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, 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, 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

Offset: 1

Author

Jason Earls, Sep 15 2002

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Jason Earls, Some Smarandache-type sequences and problems concerning abundant and deficient numbers, in Smarandache Notions Journal (2004), Vol. 14.1, pp 265-270.

Programs

Maple

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

Mathematica

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 *)