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Search: id:A089195
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| A089195 |
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Primes p such that p-1 has square factors only. |
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+0
1
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| 5, 37, 101, 197, 677, 4357, 5477, 8837, 12101, 16901, 17957, 21317, 28901, 42437, 44101, 52901, 98597, 106277, 148997, 164837, 184901, 217157, 220901, 224677, 324901, 401957, 417317, 427717, 454277, 476101, 509797, 682277, 792101, 820837
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This property for prime p-1 = cube only numbers does not hold since the sum of 2 cubes has factors and p-1 = q^3 => p = q^3+1 = sum of 2 cubes.
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EXAMPLE
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101 is included because 100 = 2^2*5^2 only square factors. 109 is not because
while 108=2^2*3^3 has a square only factor it also has a cube factor.
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PROGRAM
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(PARI) \ Input number of iterations n, power p and number to subtract k. powerfreep3(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(!ispowerfree3(x-k, p), c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) } ispowerfree3(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] == p1, flag=0, flag=1; break); ); return(flag) }
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CROSSREFS
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Sequence in context: A054587 A099937 A142036 this_sequence A023289 A006468 A095924
Adjacent sequences: A089192 A089193 A089194 this_sequence A089196 A089197 A089198
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2003
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