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

Author

Franz Vrabec, Jan 03 2006

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A114871, A114873.

Programs

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 *)

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

Extensions

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