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A141565
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Add 1 to all bases and exponents which are greater than 1 in the prime number decomposition of n.
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1
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2, 3, 4, 27, 6, 12, 8, 81, 64, 18, 12, 108, 14, 24, 24, 243, 18, 192, 20, 162, 32, 36, 24, 324, 216, 42, 256, 216, 30, 72, 32, 729, 48, 54, 48, 1728, 38, 60, 56, 486, 42, 96, 44, 324, 384, 72, 48, 972, 512, 648, 72, 378, 54, 768, 72, 648, 80, 90, 60, 648, 62, 96, 512
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OFFSET
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1,1
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COMMENTS
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Start from the prime number decomposition of n, that is the list 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3... Add 1 to all visible bases and exponents (visible in the sense that exponents are not written down if they equal 1), that is 1+1, 2+1, 3+1, (2+1)^(2+1), 5+1, (2+1)*(3+1), 7+1, (2+1)^(3+1), (3+1)^(2+1), (2+1)*(5+1), 11+1, (2+1)^(2+1)*(3+1)..). Evaluate this modified product to yield a(n).
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LINKS
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MAPLE
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A := proc(n) local a, p, e, q, ifs ; ifs := ifactors(n)[2] ; if n = 1 then RETURN(2) fi; a := 1; for p in ifs do q := op(1, p)+1 ; if op(2, p) > 1 then e := op(2, p)+1 ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 120 do printf("%d, ", A(n)) ; od: # R. J. Mathar, Aug 21 2008
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MATHEMATICA
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Array[Times @@ Apply[Times, FactorInteger[#] /. {{p_, e_} /; e > 1 :> (p + 1)^(e + 1), {k_, 1} :> k + 1}] &, 63] (* Michael De Vlieger, Nov 23 2017 *)
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PROG
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(PARI) A141565(n) = { if(1==n, return(2)); my(f=factor(n)); for(i=1, omega(n), f[i, 1] += 1; if(f[i, 2]>1, f[i, 2] += 1)); factorback(f); }; \\ Antti Karttunen, Nov 23 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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