A277804 Numbers n such that first digit of n divides n, last digit of n divides n, number of divisors of n divides n and phi(n) divides n, where phi(n) is the Euler totient function.

1, 2, 8, 12, 24, 36, 128, 288, 384, 864, 972, 1152, 1944, 3456, 6144, 6912, 13122, 18432, 26244, 31104, 62208, 69984, 209952, 279936, 294912, 497664, 839808, 884736, 1679616, 3538944, 4478976, 13436928, 22674816, 25165824, 31850496, 45349632

Offset: 1

Author

Ilya Gutkovskiy, Nov 01 2016

Keywords

• nonn
• base

Comments

Numbers n such that A000030(n)|n, A010879(n)|n, A000005(n)|n and A000010(n)|n.

Intersection of A007694, A034709, A033950 and A034837.

Examples

			a(5) = 24 because 24/2 = 12, 24/4 = 6, 24 has 8 divisors {1,2,3,4,6,8,12,24}, 24/8 = 3, phi(24) = 8 {1,5,7,11,13,17,19,23} and 24/8 = 3 (all are an integers).
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..43
• Index to divisibility sequences

Crossrefs

Cf. A000005, A000010, A000030, A007694, A034709, A033950, A034837, A010879.

Programs

Mathematica

Select[Range[50000000], Divisible[#1, First[IntegerDigits[#1]]] && Divisible[#1, Last[IntegerDigits[#1]]] && Divisible[#1, DivisorSigma[0, #1]] && Divisible[#1, EulerPhi[#1]] & ]

Extensions

a(24) - a(36) added by G. C. Greubel, Nov 02 2016