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A063775
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Number of 4th powers dividing n.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,16
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,2000
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FORMULA
| a(n) = A000005(A053164(n)) = A046951(A000188(n)). Multiplicative with a(p^e) = 1+floor(e/4).
Dirichlet g.f. zeta^2(4s)*product_{primes p} (1+p^(-s) + p^(-2s) + p^(-3s)). - R. J. Mathar, Jan 11 2012
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EXAMPLE
| a(79) = 1 since 79 is divisible by 1 = 1^4; a(80) = 2 since 80 is divisible by 1 and 16 = 2^4; a(81) = 2 since 81 is divisible by 1 and 81 = 3^4.
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PROG
| (PARI) { for (n=1, 2000, k=2; a=1; while ((p=k^4) <= n, if (n%p == 0, a++); k++); write("b063775.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 30 2009]
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CROSSREFS
| Cf. A046951, A061704.
Sequence in context: A194333 A203640 A043289 * A053164 A055229 A062379
Adjacent sequences: A063772 A063773 A063774 * A063776 A063777 A063778
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KEYWORD
| mult,easy,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Aug 16 2001
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