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A372566
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Numbers k such that k, sigma(k) and A003961(k) have a common divisor larger than 1, where A003961(n) is fully multiplicative function with a(prime(i)) = prime(i+1).
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3
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6, 18, 24, 30, 42, 54, 60, 66, 72, 78, 90, 96, 102, 114, 120, 126, 132, 135, 138, 140, 150, 162, 168, 174, 180, 186, 198, 204, 210, 216, 222, 234, 240, 246, 258, 264, 270, 276, 282, 285, 288, 294, 306, 312, 318, 330, 342, 348, 354, 360, 366, 378, 384, 390, 396, 402, 408, 414, 420, 426, 435, 438, 450, 455, 456, 462
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OFFSET
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1,1
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LINKS
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EXAMPLE
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24 = 2^3 * 3, sigma(24) = 60 = 2^2 * 3 * 5, and A003961(24) = 135 = 3^3 * 5, have 3 as their common divisor, therefore 24 is present in this sequence.
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PROG
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(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA372566(n) = (1<gcd([n, sigma(n), A003961(n)]));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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