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A086664
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n - {sum of prime power components of n}.
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1
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1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 5, 0, 5, 7, 0, 0, 7, 0, 11, 11, 9, 0, 13, 0, 11, 0, 17, 0, 20, 0, 0, 19, 15, 23, 23, 0, 17, 23, 27, 0, 30, 0, 29, 31, 21, 0, 29, 0, 23, 31, 35, 0, 25, 39, 41, 35, 27, 0, 48
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,10
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COMMENTS
| a(n) = 0 iff n is a prime power p^a, a >= 1.
Contribution from Daniel Forgues (squid(AT)zensearch.com), Nov 16 2009: (Start)
a(n) = {product of prime power components of n} - {sum of prime power components of n}.
a(1) = {product of prime power components of 1} - {sum of prime power components of 1}
a(1) = {empty product} - {empty sum} = 1 - 0 = 1 (End)
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..100000
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FORMULA
| n - A008475(n).
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EXAMPLE
| a(1)=1-(0)=1, a(8)=8-(2^3)=0, a(10)=10-(2^1+5^1)=3
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PROG
| (PARI) sof(n)=local(x); x=factor(n); sum(i=1, length(x[, 1]), x[i, 1]^x[i, 2]); for(i=1, 60, print1(i-sof(i)", "))
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CROSSREFS
| Cf. A008475.
Sequence in context: A058026 A004605 A175919 * A164736 A109753 A167465
Adjacent sequences: A086661 A086662 A086663 * A086665 A086666 A086667
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KEYWORD
| nonn
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Jul 27 2003
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EXTENSIONS
| Corrected (changed a(1) from 0 to 1) and edited by Daniel Forgues (squid(AT)zensearch.com), Nov 14 2009
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