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0, 0, 1, 1, 3, 2, 5, 4, 6, 6, 9, 6, 11, 10, 11, 11, 15, 12, 17, 14, 17, 18, 21, 16, 22, 22, 23, 22, 27, 22, 29, 26, 29, 30, 31, 27, 35, 34, 35, 32, 39, 34, 41, 38, 39, 42, 45, 38, 46, 44, 47, 46, 51, 46, 51, 48, 53, 54, 57, 48, 59, 58, 57, 57, 61, 58, 65
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| a(n) = number of non-divisors of n in 1..n. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 14 2009]
Also equal to the number of partitions p of n such that max(p)-min(p) = 1. The number of partitions of n with max(p)-min(p) <= 1 is n; there is one with k parts for each 1 <= k <= n. max(p)-min(p) = 0 iff k divides n, leaving n-d(n) with a difference of 1. It is easiest to see this by looking at fixed k with increasing n: for k=3, starting with n=3 the partitions are [1,1,1], [2,1,1], [2,2,1], [2,2,2], [3,2,2], etc. - Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 06 2006 and Franklin T. Adams-Watters, Jan 30 2011.
a(n)=number of positive numbers in n-th row of array T given by A049816.
a(n) = SUM(A000007(A051731(n,k)): 1<=k<=n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 09 2010]
a(n) is the number of proper non-divisors of n. [From Omar E. Pol (info(AT)polprimos.com), May 25 2010]
a(n) = A076627(n) / A000005(n). [Reinhard Zumkeller, Feb 06 2012]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n)=sum(k=1, n, ceil(n/k)-floor(n/k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 11 2003
G:=sum(x^(2*k+1)/(1-x^k)/(1-x^(k+1)),k=1..infinity); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2006
a(n) = A006590(n) - A006218(n) = A161886(n) - A000005(n) - A006218(n) + 1 for n >= 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 14 2009]
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EXAMPLE
| a(7) = 5; the 5 non-divisors of 7 in 1..7 are 2, 3, 4, 5, and 6.
The 5 partitions of 7 with max(p) - min(p) = 1 are [4,3],[3,2,2],[2,2,2,1],[2,2,1,1,1] and [2,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2006
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MAPLE
| with(numtheory); A049820 := n->n-sigma[0](n);
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PROG
| (PARI) a(n)=n-numdiv(n)
(Haskell)
a049820 n = n - a000005 n -- Reinhard Zumkeller, Feb 06 2012
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CROSSREFS
| Cf. A000005, A062249.
Cf. A173540, A173541. [From Omar E. Pol (info(AT)polprimos.com), May 25 2010]
Sequence in context: A062327 A075491 A089279 * A109712 A095049 A118209
Adjacent sequences: A049817 A049818 A049819 * A049821 A049822 A049823
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 30 2012
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