A238225 - OEIS

A238225

Composite numbers n such that if x = sigma(n)-phi(n)-n then n = sigma(x)-phi(x)-x.

12, 42, 1242, 2010, 2358, 57990, 65802, 1782198, 1890738, 2504920, 2733880, 3286128, 4181968, 6137440, 7861200, 8233134, 11208018, 15228688, 21445340, 24563812, 33714690, 38928126, 185154858, 207494658, 221604534, 247017798, 341398422, 366777018

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A088826 is a subset of this sequence: it lists the fixed points of the transform n -> sigma(n)-phi(n)-n.

a(29) > 10^9. - Michel Marcus, Mar 06 2014

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

Fixed points: 12, 42, 1242, 6137440, 1385119360, ...

sigma(2010) = 4896, phi(2010) = 528 and 4896 - 528 - 2010 = 2358.

sigma(2358) = 5148, phi(2358) = 780 and 5148 - 780 - 2358 = 2010.

MAPLE

with(numtheory); P:=proc(q)local a, n;

for n from 1 to q do a:=sigma(n)-phi(n)-n;

if a>0 and sigma(a)-phi(a)-a=n then print(n);

fi; od; end: P(10^6);

PROG

(PARI) isok(n) = !isprime(n) && ((x = (sigma(n) - eulerphi(n) - n)) > 0) && (n == (sigma(x) - eulerphi(x) - x)); \\ Michel Marcus, Mar 06 2014

CROSSREFS

Cf. A000010, A000203, A088826, A238226-A238230.

Sequence in context: A122973 A074356 A172294 * A088826 A125221 A253911

Adjacent sequences: A238222 A238223 A238224 * A238226 A238227 A238228

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Feb 20 2014

EXTENSIONS

a(8)-a(28) from Michel Marcus, Mar 06 2014

STATUS

approved