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A073716 Numbers n such that the number of prime divisors of n (counted with multiplicity) = number of anti-divisors of n. 0
1, 3, 9, 20, 30, 40, 44, 80, 84, 100, 114, 168, 174, 192, 208, 244, 256, 272, 300, 316, 324, 404, 440, 456, 464, 520, 524, 596, 672, 704, 720, 834, 894, 1044, 1064, 1248, 1272, 1324, 1416, 1464, 1604, 1608, 1626, 1632, 1636, 1680, 1686, 1704, 1744, 1756 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A066272 for definition of anti-divisor.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

40 is a term since its prime factors are {2, 2, 2, 5} and its anti-divisors are {3, 9, 16, 27}.

MATHEMATICA

atd[n_] := Count[Flatten[Quotient[#, Rest[Select[Divisors[#], OddQ]]] & /@ (2 n + Range[-1, 1])], Except[1]]; Select[Range[1760], PrimeOmega[#] == atd[#] &] (* Jayanta Basu, Jul 08 2013 *)

PROG

(PARI) {for(n=1, 1800, v1=[]; v2=[]; v3=[]; ds=divisors(2*n-1); for(k=2, matsize(ds)[2]-1, if(ds[k]%2>0, v1=concat(v1, ds[k]))); ds=divisors(2*n); for(k=2, matsize(ds)[2]-1, if(ds[k]%2>0, v2=concat(v2, ds[k]))); ds=divisors(2*n+1); for(k=2, matsize(ds)[2]-1, if(ds[k]%2>0, v3=concat(v3, ds[k]))); v=vecsort(concat(v1, concat(v2, v3))); if(matsize(v)[2]==bigomega(n), print1(n, ", ")))}

CROSSREFS

Cf. A001222, A066272.

Sequence in context: A178963 A033315 A200612 * A174866 A187409 A037048

Adjacent sequences:  A073713 A073714 A073715 * A073717 A073718 A073719

KEYWORD

nonn

AUTHOR

Jason Earls, Aug 30 2002

EXTENSIONS

Edited and extended by Klaus Brockhaus, Sep 02 2002

STATUS

approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)