cp's OEIS Frontend

A331669 List of distinct numbers that occur in A318366 (the Dirichlet convolution square of bigomega).

%I A331669 #79 May 05 2020 22:24:50
%S A331669 0,1,2,4,8,10,12,20,24,34,35,40,48,52,56,70,72,84,95,104,112,116,120,
%T A331669 130,156,160,164,165,168,180,189,212,220,224,238,240,258,280,284,286,
%U A331669 300,304,322,330,344,348,352,364,380,420,438,440,455,460,464,472,477,480
%N A331669 List of distinct numbers that occur in A318366 (the Dirichlet convolution square of bigomega).
%C A331669 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 A331669 Terms of this sequence select from the positive integers as follows:
%C A331669 A318366(k) = a(1), 1 followed by the primes (A008578).
%C A331669 A318366(k) = A008836(k) = A001221(k) = a(2), primes squared (A001248).
%C A331669 A318366(k) = A001221(k) = a(3), squarefree semiprimes (A006881).
%C A331669 A318366(k) = A000005(k) = a(4), primes cubed (A030078).
%C A331669 A318366(k) = a(5), a prime squared times a prime (A054753).
%C A331669 A318366(k) = a(6), primes to the fourth power (A030514).
%C A331669 A318366(k) = a(7), sphenic numbers (A007304).
%C A331669 A318366(k) = a(8), union of A050997 and A065036.
%C A331669 A318366(k) = a(9), squarefree semiprimes squared (A085986).
%C A331669 A318366(k) = a(10), product of four primes, three distinct (A085987).
%C A331669 A318366(k) = a(11), primes to the sixth power (A030516).
%C A331669 A318366(k) = a(12), product of prime to fourth power and a different prime (A178739).
%C A331669 A318366(k) = a(13), product of four distinct primes (A046386).
%C A331669 ...
%e A331669 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 A331669 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 A331669 Cf. A001222, A318366.
%Y A331669 Cf. also A101296.
%K A331669 nonn
%O A331669 1,3
%A A331669 _Torlach Rush_, Jan 23 2020
%E A331669 More terms, using A318366 extended b-file, from _Michel Marcus_, Jan 24 2020