A280350 - OEIS

%I #11 Sep 08 2022 08:46:18

%S 79228162514264337593543950336,

%T 6362685441135942358474828762538534230890216321,

%U 12621774483536188886587657044524579674771302961744368076324462890625,1347137238494276547832006567721872890819326613454654477690085519113574118965817601,9412343651268540526001186511911506574868063110469548823950876000379062365652829504091329792873336961

%N Numbers with 97 divisors.

%C Also, 96th powers of primes.

%C More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 97.

%H OEIS Wiki, <a href="https://oeis.org/wiki/Index_entries_for_number_of_divisors">Index entries for number of divisors</a>

%F a(n) = A000040(n)^(97-1) = A000040(n)^96.

%F A000005(a(n)) = 97.

%e a(1) = 2^96, a(2) = 3^96, a(3) = 5^96, a(4) = 7^96, a(5) = 11^96.

%t With[{p = 25}, Table[Prime[n]^(Prime[p] - 1), {n, 5}]] (* _Michael De Vlieger_, Jan 02 2017 *)

%o (PARI) a(n)=prime(n)^96

%o (Magma) [NthPrime(n)^96: n in [1..5]]; // _Vincenzo Librandi_, Jan 06 2017

%Y Cf. A000005, A000040, A001248, A030514, A030516, A030629, A030631, A030635, A030637, A137486, A137492, A139571, A139572, A139573, A139574, A139575, A173533, A183062, A183085, A280298, A280299, A280301, A280346, A280347, A280349, A261700.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Jan 02 2017