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

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325369 Numbers with no two prime exponents appearing the same number of times in the prime signature. 6
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 84, 85, 86 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The prime signature (A118914) is the multiset of exponents appearing in a number's prime factorization. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose multiplicities appear with distinct multiplicities. The enumeration of these partitions by sum is given by A325329. LINKS EXAMPLE Most small numbers are in the sequence. However the sequence of non-terms together with their prime indices begins:   12: {1,1,2}   18: {1,2,2}   20: {1,1,3}   24: {1,1,1,2}   28: {1,1,4}   40: {1,1,1,3}   44: {1,1,5}   45: {2,2,3}   48: {1,1,1,1,2}   50: {1,3,3}   52: {1,1,6}   54: {1,2,2,2}   56: {1,1,1,4}   63: {2,2,4}   68: {1,1,7}   72: {1,1,1,2,2}   75: {2,3,3}   76: {1,1,8}   80: {1,1,1,1,3}   88: {1,1,1,5} For example, the prime indices of 1260 are {1,1,2,2,3,4}, whose multiplicities give the prime signature {1,1,2,2}, and since 1 and 2 appear the same number of times, 1260 is not in the sequence. MATHEMATICA Select[Range[100], UnsameQ@@Length/@Split[Sort[Last/@FactorInteger[#]]]&] CROSSREFS Cf. A056239, A098859, A112798, A118914, A130091, A317090, A319161, A325326, A325329, A325331, A325337, A325370, A325371. Sequence in context: A263837 A283550 A271113 * A317101 A304449 A085924 Adjacent sequences:  A325366 A325367 A325368 * A325370 A325371 A325372 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 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 January 18 13:30 EST 2020. Contains 331007 sequences. (Running on oeis4.)