A039777 Integers m such that phi(m) is equal to the sum of (the product of prime factors) and (the product of exponents) of m-1.

2, 5, 21, 45, 285, 765, 27645, 196605, 41067645, 72787965, 250871805, 4295098365, 12884901885, 23307153405, 172130669565, 1766029428523005, 20978888016396285

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• more
• hard

Comments

No other terms below 10^24. Some large terms: 1039619980803100740810795122685, 32576974833437288924302842789885. - Max Alekseyev, Jul 28 2024

All listed terms represent solutions to phi(m) = (m+3)/2 such that (m-1)/2 is an even squarefree number. Cf. A350777. - Max Alekseyev, Jul 21 2024

a(1)=2 is the only even term below 10^100000. - Max Alekseyev, Jul 22 2024

Examples

			21 is a term since 21-1 = 2^2*5^1 and (2*5)+(2*1) = 12 = phi(21).
		

Crossrefs

Cf. A000010, A039696, A350777.

Extensions

More terms from Jud McCranie

Corrected example and a(11)-a(14) from Donovan Johnson, Nov 14 2010

a(15)-a(17) from Max Alekseyev, Jul 21 2024