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Search: id:A079142
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| A079142 |
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Numbers divisible by prime integer parts of their square roots. |
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+0
1
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| 4, 6, 8, 9, 12, 15, 25, 30, 35, 49, 56, 63, 121, 132, 143, 169, 182, 195, 289, 306, 323, 361, 380, 399, 529, 552, 575, 841, 870, 899, 961, 992, 1023, 1369, 1406, 1443, 1681, 1722, 1763, 1849, 1892, 1935, 2209, 2256, 2303, 2809, 2862, 2915, 3481, 3540, 3599
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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n is in the sequence if r=floor(sqrt(n)) is prime and r divides n.
Union of the 3 sequences A001248={p^2}, A036690={p(p+1)}, and {p(p+2)} for p prime.
The sum of the reciprocals = 1.04...
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FORMULA
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a(n) = prime(floor(n/3+1))*(prime(floor(n/3+1)) + (n mod 3))
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EXAMPLE
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56 is in the sequence because floor(sqrt(56)) = 7 is prime and 7 divides 56.
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MATHEMATICA
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Flatten[ #(#+{0, 1, 2})&/@Prime/@Range[20]]
a[n_] := (p=Prime[Floor[n/3+1]])(p+Mod[n, 3])
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PROGRAM
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(PARI) ipsqrt(n) = { sr= 0; for(x=1, n, v = floor(sqrt(x)); if(isprime(v) && x%v == 0, print1(x" "); sr+=1.0/x; ); ); print(); print(sr); } \\ numbers divisible by prime integer parts of their square roots.
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CROSSREFS
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Adjacent sequences: A079139 A079140 A079141 this_sequence A079143 A079144 A079145
Sequence in context: A067012 A122786 A092630 this_sequence A062002 A028958 A036310
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 26 2002
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