A076702 Distinct-digit prime powers of prime numbers.

4, 8, 9, 25, 27, 32, 49, 125, 128, 169, 243, 289, 361, 529, 841, 961, 1369, 1849, 2048, 2187, 2197, 2809, 3125, 3481, 3721, 4913, 5041, 5329, 6241, 6859, 7921, 8192, 12769, 16807, 18769, 24389, 32041, 32761, 36481, 37249, 39601, 54289, 68921

Offset: 1

Author

Zak Seidov, Oct 26 2002

Keywords

• nonn
• base
• fini
• full

Comments

Up to 10^10, there are only 108 distinct-digit prime powers of prime numbers; the last one being 2^29 = 536870912.

Links

• Ray Chandler, Table of n, a(n) for n = 1..108 (full sequence)

Crossrefs

Cf. A053810, A075308.

Programs

Mathematica

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^10]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^10]]]}]]]; a = {}; Do[ d = IntegerDigits[ pp[[n]]]; If[ Length[d] == Length[ Union[d]], a = Append[a, pp[[n]]]], {n, 1, 9965}]; a

Extensions

Edited by Robert G. Wilson v, Oct 31 2002