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A065773
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Number of divisors of square of true prime powers arising in A065405.
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0
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5, 7, 7, 5, 13, 7, 5, 17, 5, 19, 5, 13, 5, 5, 7, 11, 7, 5, 5, 5, 13, 5, 7, 31, 5, 5, 5, 5, 5, 5, 13, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n)=A000005[A065405(n)^2], If A065405(n)=q^c, a prime-power, then sigma[q^(2c)]=A000203[q^(2c)]=[ -1+q^(2c+1)]/(q-1) =[ -1+q^A000005(A065405(n)^2)]/(q-1) also a prime, from A065403.
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EXAMPLE
| n = 3125, tau[nn] = 11, sigma[nn] = 12207031 = (5^(tau[nn])-1)/4 = A065403[16] is also a prime.
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PROG
| (PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), a=numdiv(m^2); write("b065773.txt", n++, " ", a); if (n==100, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 30 2009]
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CROSSREFS
| Cf. A000005, A065405, A000203, A065771, A065772, A025475.
DivisorSigma[0, (A065405)^2].
Sequence in context: A020760 A011269 A093723 * A114916 A001989 A086056
Adjacent sequences: A065770 A065771 A065772 * A065774 A065775 A065776
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 19 2001
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