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A092976
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Consider all partitions of n into parts all of which are divisors of n; a(n) = number of distinct values taken by the product of the parts.
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0
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1, 2, 2, 3, 2, 7, 2, 5, 4, 10, 2, 19, 2, 13, 13, 9, 2, 37, 2, 29, 17, 19, 2, 61, 6, 22, 10, 39, 2, 247, 2, 17, 25, 28, 25, 127, 2, 31, 29, 97, 2, 450, 2, 59, 82, 37, 2, 217, 8, 146, 37, 69, 2, 271, 37, 133, 41, 46, 2, 1558, 2, 49, 112, 33, 43, 1038, 2, 89, 49, 1105, 2, 469, 2, 58, 211, 99, 49, 1423, 2, 353
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) > tau(n)+ A(n) + R(n), where tau(n) = number of divisors of n, A(n)= product of powers of nontrivial divisors whose sum with multiplicity is < n and R(n) = numbers of the form r^(k)> n where r is a divisor of n and k <= n/r.
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EXAMPLE
| a(10) = 10, the numbers arising are 1,2,4,5,8,10,16,20,25 and 32; e.g. 25 = 5*5, 8 = 2*2*2*1*1*1*1, 32 = 2*2*2*2*2, etc.
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MAPLE
| with (numtheory):
a:= proc(n) local b, l, s;
l:= sort ([divisors(n)[]]);
b:= proc(n, i, p)
if n<0 then
elif n=0 then s:= s union {p}
elif i=0 then
else b(n-l[i], i, p*l[i]); b(n, i-1, p)
fi
end;
s:= {};
b(n, nops(l), 1);
nops(s)
end:
seq (a(n), n=1..60); # Alois P. Heinz, Feb 21, 2011
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CROSSREFS
| Cf. A092975.
Sequence in context: A094438 A156098 A015996 * A084705 A141652 A117754
Adjacent sequences: A092973 A092974 A092975 * A092977 A092978 A092979
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2004
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2005
More terms and Maple program from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 21 2011
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