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List of distinct numbers that occur in A318366 (the Dirichlet convolution square of bigomega).
0

%I #79 May 05 2020 22:24:50

%S 0,1,2,4,8,10,12,20,24,34,35,40,48,52,56,70,72,84,95,104,112,116,120,

%T 130,156,160,164,165,168,180,189,212,220,224,238,240,258,280,284,286,

%U 300,304,322,330,344,348,352,364,380,420,438,440,455,460,464,472,477,480

%N List of distinct numbers that occur in A318366 (the Dirichlet convolution square of bigomega).

%C There is a strong correlation between values of this function and values of other arithmetic functions. In other words, a(n) correlates to a single distinct value from one or more of the arithmetic functions.

%C Terms of this sequence select from the positive integers as follows:

%C A318366(k) = a(1), 1 followed by the primes (A008578).

%C A318366(k) = A008836(k) = A001221(k) = a(2), primes squared (A001248).

%C A318366(k) = A001221(k) = a(3), squarefree semiprimes (A006881).

%C A318366(k) = A000005(k) = a(4), primes cubed (A030078).

%C A318366(k) = a(5), a prime squared times a prime (A054753).

%C A318366(k) = a(6), primes to the fourth power (A030514).

%C A318366(k) = a(7), sphenic numbers (A007304).

%C A318366(k) = a(8), union of A050997 and A065036.

%C A318366(k) = a(9), squarefree semiprimes squared (A085986).

%C A318366(k) = a(10), product of four primes, three distinct (A085987).

%C A318366(k) = a(11), primes to the sixth power (A030516).

%C A318366(k) = a(12), product of prime to fourth power and a different prime (A178739).

%C A318366(k) = a(13), product of four distinct primes (A046386).

%C ...

%e 0 is a term because the only divisors of a prime (p) are 1 and a prime itself and bigomega(1) * bigomega(p) + bigomega(p) * bigomega(1) = 0 * 1 + 1 * 0 = 0.

%e 1 is a term because a prime squared gives bigomega(1) * bigomega(p^2) + bigomega(p) * bigomega(p) + bigomega(p^2) * bigomega(1) = 0 * 2 + 1 * 1 + 2 * 0 = 1.

%Y Cf. A001222, A318366.

%Y Cf. also A101296.

%K nonn

%O 1,3

%A _Torlach Rush_, Jan 23 2020

%E More terms, using A318366 extended b-file, from _Michel Marcus_, Jan 24 2020