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A072627
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Number of divisors d of n such that d-1 is prime.
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2
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0, 0, 1, 1, 0, 2, 0, 2, 1, 0, 0, 4, 0, 1, 1, 2, 0, 3, 0, 2, 1, 0, 0, 6, 0, 0, 1, 2, 0, 3, 0, 3, 1, 0, 0, 5, 0, 1, 1, 3, 0, 4, 0, 2, 1, 0, 0, 7, 0, 0, 1, 1, 0, 4, 0, 3, 1, 0, 0, 7, 0, 1, 1, 3, 0, 2, 0, 2, 1, 1, 0, 8, 0, 1, 1, 2, 0, 2, 0, 4, 1, 0, 0, 7, 0, 0, 1, 3, 0, 5, 0, 1, 1, 0, 0, 8, 0, 2, 1, 2, 0, 3, 0, 3, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| A001221[InvSigma[n]] < A000005[n]
Inverse Mobius transform of A010051. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 25 2009]
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EXAMPLE
| If n=p is prime then divisors-1={1,p}-1={0,p-1} so a(p)=0. n=240: a(240)=12 because primes of -1+d form are: {2,3,5,7,11,19,23,29,47,59,79,239}. These and only these divisors are present in any InvSigma of n, like:InvSig[240]= {114,135,158,177,203,209,239} with {2,3,19,3,5,2,79,3,59,7,29,11,19,239} p-divisors.
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MATHEMATICA
| di[x_] := Divisors[x] dp[x_] := Part[di[x], Flatten[Position[PrimeQ[ -1+di[x]], True]]]-1 Table[Length[dp[w]], {w, 1, 128}]
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CROSSREFS
| Cf. A000203, A000005.
Sequence in context: A006996 A112604 A203399 * A069848 A194702 A118682
Adjacent sequences: A072624 A072625 A072626 * A072628 A072629 A072630
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 28 2002
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