A195943 Zeroless prime powers: Intersection of A000961 and A052382.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, 256, 257, 263, 269, 271, 277, 281, 283, 289, 293, 311

Offset: 1

Author

M. F. Hasler, Sep 25 2011

Keywords

• nonn
• base

Comments

In contrast to A195942, we also allow for primes (p^n with n=1) in this sequence.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• C. Rivera, Puzzle 607. A zeroless Prime power, on primepuzzles.net, Sept. 24, 2011.

Crossrefs

Cf. A195942, A195944, A195945, A195946, A195908, A195948, A007377, A008839, A030700, A030701, A030702, A030703, A030704, A030705, A030706.

Cf. A038618 (subsequence).

Programs

Haskell

a195943 n = a195943_list !! (n-1)
a195943_list = filter ((== 1) . a010055) a052382_list
-- Reinhard Zumkeller, Sep 27 2011

PARI

for( n=1,9999, is_A000961(n) && is_A052382(n) && print1(n","))

Formula

A195943 = A000961 intersect A052382 = A000961 \ A011540.

A010055(a(n)) * A168046(a(n)) = 1. - Reinhard Zumkeller, Sep 27 2011