OFFSET
1,2
COMMENTS
The first arithmetic derivation of products of 2 successive prime numbers (A006094) is the sum of 2 successive prime numbers (A001043). A001043 = (A006094)’. The second arithmetic derivation is (A240052) = (A001043)’ = (A006094)’’. The third arithmetic derivation of products of 2 successive prime numbers (A006094) is a(n) = (A240052)’ = (A001043)’’ = (A006094)’’’.
LINKS
Freimut Marschner, Table of n, a(n) for n = 1..429
Wikipedia, Arithmetic derivative
Wikipedia, p-derivation
EXAMPLE
MAPLE
with(numtheory); P:= proc(q) local a, b, c, d, n, p; a:=ithprime(n)*ithprime(n+1);
for n from 1 to q do a:=ithprime(n)*ithprime(n+1);
b:=a*add(op(2, p)/op(1, p), p=ifactors(a)[2]); c:=b*add(op(2, p)/op(1, p), p=ifactors(b)[2]);
d:=c*add(op(2, p)/op(1, p), p=ifactors(c)[2]); print(d);
od; end: P(10^4); # Paolo P. Lava, Apr 07 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Freimut Marschner, Mar 31 2014
STATUS
approved