Revision History for A316413
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#17 by Alois P. Heinz at Fri Nov 19 18:54:21 EST 2021
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#16 by Alois P. Heinz at Fri Nov 19 18:54:18 EST 2021
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# second Maple program:
q:= n-> (l-> nops(l)>0 and irem(add(i, i=l), nops(l))=0)(map
(i-> numtheory[pi](i[1])$i[2], ifactors(n)[2])):
select(q, [$1..110])[]; # Alois P. Heinz, Nov 19 2021
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| STATUS
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approved
editing
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#15 by R. J. Mathar at Fri Aug 09 12:27:03 EDT 2019
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#14 by R. J. Mathar at Fri Aug 09 12:26:56 EDT 2019
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| LINKS
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R. J. Mathar, <a href="/A316413/b316413.txt">Table of n, a(n) for n = 1..1327</a>
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| MAPLE
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isA326413 := proc(n)
psigsu := A056239(n) ;
psigle := numtheory[bigomega](n) ;
if modp(psigsu, psigle) = 0 then
true;
else
false;
end if;
end proc:
n := 1:
for i from 2 to 3000 do
if isA326413(i) then
printf("%d %d\n", n, i);
n := n+1 ;
end if;
end do: # R. J. Mathar, Aug 09 2019
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approved
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#13 by N. J. A. Sloane at Mon Jul 02 22:39:29 EDT 2018
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#12 by Gus Wiseman at Mon Jul 02 21:35:24 EDT 2018
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#11 by Gus Wiseman at Mon Jul 02 12:23:29 EDT 2018
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| CROSSREFS
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Cf. A056239, A067538, A074761, A143773, A237984, A289508, A289509, A290103, A296150, A298423, A316428, A316431.
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#10 by Gus Wiseman at Mon Jul 02 11:10:21 EDT 2018
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| NAME
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allocatedHeinz numbers of integer partitions whose length fordivides Gustheir Wisemansum.
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| DATA
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2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 37, 39, 41, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62, 64, 67, 68, 71, 73, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 94, 97, 98, 99, 100, 101, 103, 105, 107, 109, 110
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| OFFSET
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1,1
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| COMMENTS
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In other words, partitions whose average is an integer.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
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| EXAMPLE
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Sequence of partitions whose length divides their sum begins (1), (2), (11), (3), (4), (111), (22), (31), (5), (6), (1111), (7), (8), (42), (51), (9), (33), (222), (411).
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| MATHEMATICA
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Select[Range[2, 100], Divisible[Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]], PrimeOmega[#]]&]
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Cf. A056239, A067538, A074761, A143773, A237984, A289509, A296150, A298423.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Gus Wiseman, Jul 02 2018
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| STATUS
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approved
editing
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#9 by Gus Wiseman at Mon Jul 02 11:10:21 EDT 2018
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allocated for Gus Wiseman
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recycled
allocated
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#8 by N. J. A. Sloane at Mon Jul 02 06:56:22 EDT 2018
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