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

1,2

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.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..43

Index to divisibility sequences

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A280252 A013654 A359964 * A108978 A269968 A135957

Adjacent sequences: A277801 A277802 A277803 * A277805 A277806 A277807

Keyword

nonn,base

Author

Ilya Gutkovskiy, Nov 01 2016

Extensions

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

Status

approved