

A245497


a(n) = phi(n)^2/2, where phi(n) = A000010(n), the Euler totient function.


2



2, 2, 8, 2, 18, 8, 18, 8, 50, 8, 72, 18, 32, 32, 128, 18, 162, 32, 72, 50, 242, 32, 200, 72, 162, 72, 392, 32, 450, 128, 200, 128, 288, 72, 648, 162, 288, 128, 800, 72, 882, 200, 288, 242, 1058, 128, 882, 200, 512, 288, 1352, 162, 800, 288, 648, 392, 1682
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

3,1


COMMENTS

Values of a(n) < 3 are nonintegers since phi(1) = phi(2) = 1 (odd). Since phi(n) is even for all n > 2, a(n) is a positive integer.
a(n) gives the sum of all the parts in the partitions of phi(n) with exactly two parts (see example).
a(n) is also the area of a square with diagonal phi(n).


LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 3..10000


FORMULA

a(n) = phi(n)^2/2 = A000010(n)^2/2 = A127473(n)/2, n > 2.


EXAMPLE

a(5) = 8; since phi(5)^2/2 = 4^2/2 = 8. The partitions of phi(5) = 4 into exactly two parts are: (3,1) and (2,2). The sum of all the parts in these partitions gives: 3+1+2+2 = 8.
a(7) = 18; since phi(7)^2/2 = 6^2/2 = 18. The partitions of phi(7) = 6 into exactly two parts are: (5,1), (4,2) and (3,3). The sum of all the parts in these partitions gives: 5+1+4+2+3+3 = 18.


MAPLE

with(numtheory): 245497:=n>phi(n)^2/2: seq(245497(n), n=3..50);


MATHEMATICA

Table[EulerPhi[n]^2/2, {n, 3, 50}]


PROG

(PARI) vector(100, n, eulerphi(n+2)^2/2) \\ Derek Orr, Aug 04 2014


CROSSREFS

Cf. A000010, A127473.
Sequence in context: A098984 A088560 A222821 * A086328 A095997 A274139
Adjacent sequences: A245494 A245495 A245496 * A245498 A245499 A245500


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Jul 24 2014


STATUS

approved



