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

1,10

Comments

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

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.

Example

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

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 *)

Crossrefs

Sequence in context: A060278 A046770 A046782 * A285132 A239261 A242707

Adjacent sequences: A074034 A074035 A074036 * A074038 A074039 A074040

Keyword

easy,nonn

Author

Jason Earls, Sep 15 2002

Status

approved