A159939 Odd solutions of phi(sigma(n)) = sigma(phi(n)).

9, 225, 729, 18225, 65025, 140625, 531441, 5267025, 11390625, 13286025, 18792225, 40640625, 87890625, 1522170225, 2197265625, 3291890625, 3839661225, 5430953025, 7119140625, 8303765625, 11745140625, 25400390625

Offset

1,1

Comments

sigma is the multiplicative sum-of-divisors function.

phi is Euler's totient.

Complete through 25558816403.

All given here are products of powers of consecutive Fermat primes based on generalized repunit primes; see links.

It is conjectured (see links) that all odd solutions are of this form, for which at least 10130 solutions are known.

References

Richard Guy, "Unsolved Problems in Number Theory", section B42

Oystein Ore, "Number Theory and Its History", 1948, reprinted 1988, Dover, ISBN-10: 0486656209, pp. 88 et seq., 109 et seq.

Links

Table of n, a(n) for n=1..22.

Walter Nissen, phi(sigma(n)) = sigma(phi(n))

Example

sigma(9) = 13, phi(9) = 6, sigma(6) = phi(13) = 12, so 9 is in the sequence.

Prog

(PARI) isok(n) = (n % 2) && (eulerphi(sigma(n)) == sigma(eulerphi(n))) \\ Michel Marcus, Jul 23 2013

Crossrefs

Cf. A000203, A000010, A033632, A019434.

Sequence in context: A057530 A014736 A017558 * A167038 A074190 A069075

Adjacent sequences: A159936 A159937 A159938 * A159940 A159941 A159942

Keyword

nonn

Author

Walter Nissen, Apr 26 2009

Extensions

Edited by Charles R Greathouse IV, Oct 28 2009

Status

approved