A114874 Numbers representable in exactly two ways as (p-1)*p^e (where p is a prime and e >= 0) in ascending order.

2, 4, 6, 16, 18, 42, 100, 156, 162, 256, 486, 1458, 2028, 4422, 6162, 14406, 19182, 22650, 23548, 26406, 37056, 39366, 62500, 65536, 77658, 113232, 121452, 143262, 208392, 292140, 342732, 375156, 412806, 527802, 564898, 590592, 697048, 843642

Offset

1,1

Comments

Numbers that are one less than a prime number and of the form (p-1)*p^e for some prime p and e > 0. - Jianing Song, Apr 13 2019

Links

Jianing Song, Table of n, a(n) for n = 1..162 (all terms below 10^8)

Example

6 is a member because 6 = (3-1)*3^1 = (7-1)*7^0 and 3 and 7 are primes.

Mathematica

s = Split@Sort@Flatten@Table[(Prime[n] - 1)Prime[n]^k, {n, 68000}, {k, 0, 16}]; Union@Flatten@Select[s, Length@# == 2 &] (* Robert G. Wilson v, Jan 05 2006 *)

Prog

(PARI) isA114874(n) = if(n>1, my(v=factor(n), d=#v[, 1], p=v[d, 1], e=v[d, 2]); (isprime(n+1) && n==(p-1)*p^e), 0) \\ Jianing Song, Apr 13 2019

Crossrefs

Cf. A114871, A114873.

Sequence in context: A096173 A287681 A333021 * A100361 A259939 A069654

Adjacent sequences: A114871 A114872 A114873 * A114875 A114876 A114877

Keyword

nonn

Author

Franz Vrabec, Jan 03 2006

Extensions

a(13)-a(38) from Robert G. Wilson v, Jan 05 2006

Status

approved