A240053 3rd Arithmetic derivation of products of 2 successive prime numbers (A006094).

0, 16, 32, 10, 48, 1, 92, 1, 92, 96, 156, 1, 128, 44, 188, 608, 248, 1408, 22, 1472, 240, 324, 368, 30, 86, 288, 32, 1188, 1, 1552, 30, 560, 476, 2176, 924, 476, 5120, 60, 432, 2176, 1148, 512, 4480, 1, 1300, 324, 1, 391, 1052, 46, 720, 3232, 672, 2304, 1448, 860, 2484, 1036, 226, 768, 7232, 1628

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

Formula

a(n) = (A006094(n))’’’.

a(n) = A099306(A006094(n)).

a(n) = A003415(A240052(n)).

Example

a(12)=(A006094(12))'''=(37*41)'''=(A001043(12))''=(78)''=(71)'=1;
a(14)=(A006094(14))'''=(43*47)'''=(A001043(12))''=(90)''=(123)'=44.

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

Cf. A006094, A001043, A240052.

Cf. A003415 (1st derivative), A068346 (2nd derivative), A099306 (3rd derivative).

Sequence in context: A265134 A220000 A132299 * A059164 A040240 A296761

Adjacent sequences: A240050 A240051 A240052 * A240054 A240055 A240056

Keyword

nonn

Author

Freimut Marschner, Mar 31 2014

Status

approved