The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A100778 Integer powers of primorial numbers. 13
 1, 2, 4, 6, 8, 16, 30, 32, 36, 64, 128, 210, 216, 256, 512, 900, 1024, 1296, 2048, 2310, 4096, 7776, 8192, 16384, 27000, 30030, 32768, 44100, 46656, 65536, 131072, 262144, 279936, 510510, 524288, 810000, 1048576, 1679616, 2097152, 4194304, 5336100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. 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 LINKS David A. Corneth, Table of n, a(n) for n = 1..8606 (terms <= 10^1000) FORMULA 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 EXAMPLE 10 is not a term as 6 is a member with the same prime signature 10 > 6. 216 is a term as 216 = (2*3)^3. 243 is not a term as 32 represents that prime signature. MATHEMATICA unintQ[n_]:=And[SameQ@@Last/@FactorInteger[n], Length[FactorInteger[n]]==PrimePi[FactorInteger[n][[-1, 1]]]]; Select[Range[1000], unintQ] (* Gus Wiseman, Dec 26 2018 *) CROSSREFS Cf. A000961, A001597, A002110, A007947, A025487, A055932, A056239, A057588, A072774, A072777, A112798, A304250, A319169, A322792, A322793. Sequence in context: A068799 A317306 A317087 * A324579 A271520 A122408 Adjacent sequences:  A100775 A100776 A100777 * A100779 A100780 A100781 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Nov 28 2004 EXTENSIONS More terms and simpler definition from Ray Chandler, Nov 29 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 17 09:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)