This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A100778 #31 Sep 26 2023 01:57:38
%S A100778 1,2,4,6,8,16,30,32,36,64,128,210,216,256,512,900,1024,1296,2048,2310,
%T A100778 4096,7776,8192,16384,27000,30030,32768,44100,46656,65536,131072,
%U A100778 262144,279936,510510,524288,810000,1048576,1679616,2097152,4194304,5336100
%N A100778 Integer powers of primorial numbers.
%C A100778 Smallest squarefree numbers or their powers with distinct prime signatures. Or least numbers with prime signatures (p*q*r*...)^k, where p,q,r,... are primes and k is a whole number.
%C A100778 Also Heinz numbers of uniform integer partitions whose union is an initial interval of positive integers. An integer partition is uniform if all parts appear with the same multiplicity. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). The sequence of all uniform integer partitions whose Heinz numbers belong to the sequence begins: (1), (11), (12), (111), (1111), (123), (11111), (1122), (111111), (1111111), (1234), (111222), (11111111), (111111111), (112233), (1111111111). - _Gus Wiseman_, Dec 26 2018
%C A100778 From _Amiram Eldar_, Sep 26 2023: (Start)
%C A100778 Intersection of A025487 and A072774.
%C A100778 The distinct terms of A046523(A072774(n)) in ascending orders.
%C A100778 The k-th power of the n-th primorial number, A002110(n)^k, has (k+1)^n divisors which are the set of the (k+1)-free prime(n)-smooth numbers. (End)
%H A100778 David A. Corneth, <a href="/A100778/b100778.txt">Table of n, a(n) for n = 1..8606</a> (terms <= 10^1000)
%F A100778 Sum_{n>=1} 1/a(n) = 1 + Sum_{n>=1} 1/A057588(n) = 2.2397359032... - _Amiram Eldar_, Oct 20 2020; corrected by _Hal M. Switkay_ and _Amiram Eldar_, Apr 12 2021
%e A100778 10 is not a term as 6 is a member with the same prime signature 10 > 6.
%e A100778 216 is a term as 216 = (2*3)^3. 243 is not a term as 32 represents that prime signature.
%t A100778 unintQ[n_]:=And[SameQ@@Last/@FactorInteger[n],Length[FactorInteger[n]]==PrimePi[FactorInteger[n][[-1,1]]]];
%t A100778 Select[Range[1000],unintQ] (* _Gus Wiseman_, Dec 26 2018 *)
%Y A100778 Cf. A000961, A001597, A002110, A007947, A025487, A046523, A055932, A056239, A057588, A072774, A072777, A112798, A304250, A319169, A322792, A322793.
%K A100778 easy,nonn
%O A100778 1,2
%A A100778 _Amarnath Murthy_, Nov 28 2004
%E A100778 More terms and simpler definition from _Ray Chandler_, Nov 29 2004