Revision History for A322902
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#7 by Susanna Cuyler at Mon Dec 31 13:18:24 EST 2018
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#6 by Gus Wiseman at Sun Dec 30 10:48:15 EST 2018
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#5 by Gus Wiseman at Sun Dec 30 10:47:13 EST 2018
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| EXAMPLE
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). The sequence of all integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (2), (11), (3), (4), (111), (22), (5), (6), (1111), (7), (8), (42), (9), (33), (222).
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#4 by Gus Wiseman at Sun Dec 30 09:29:28 EST 2018
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| COMMENTS
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All termsAlso arethe oddunion orof powersA322903 ofand 2A000079.
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| CROSSREFS
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Cf. A001597, A018819, A023893, A023894, A052410, A056239, A072720, A072721, A302242, A302593, A322900, A322901, A322903.
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#3 by Gus Wiseman at Sun Dec 30 09:03:44 EST 2018
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| COMMENTS
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A prime index of n is a number m such that prime(m) divides n.
A proper power of n is a number n^k for some positive integer k.
All terms are odd or powers of 2.
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#2 by Gus Wiseman at Sun Dec 30 09:01:54 EST 2018
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| NAME
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allocatedNumbers whose prime indices are all proper powers of forthe Gussame Wisemannumber.
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| DATA
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 57, 59, 61, 63, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 128, 131, 133, 137, 139, 147, 149, 151, 157, 159, 163, 167, 169
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| OFFSET
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1,2
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| EXAMPLE
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The sequence of all integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (2), (11), (3), (4), (111), (22), (5), (6), (1111), (7), (8), (42), (9), (33), (222).
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| MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All, 2]]);
Select[Range[100], SameQ@@radbase/@primeMS[#]&]
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| CROSSREFS
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Cf. A001597, A018819, A023893, A023894, A052410, A056239, A072720, A072721, A302242, A302593, A322900, A322901.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Gus Wiseman, Dec 30 2018
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| STATUS
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approved
editing
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#1 by Gus Wiseman at Sun Dec 30 09:01:54 EST 2018
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| NAME
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allocated for Gus Wiseman
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| KEYWORD
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allocated
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| STATUS
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approved
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