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a(n) = 1 if n is a product of primorial numbers (A002110), 0 otherwise.
15

%I #8 Dec 20 2018 23:19:16

%S 1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,

%T 0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,

%U 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N a(n) = 1 if n is a product of primorial numbers (A002110), 0 otherwise.

%C Characteristic function of A025487, first differences of A085089.

%C a(n) = 1 if n = 2^e1 * 3^e2 * ... * prime(k)^e_k, with k = A061395(n) = A001221(n) and e1 >= e2 >= ... >= e_k, 0 otherwise.

%H Antti Karttunen, <a href="/A322585/b322585.txt">Table of n, a(n) for n = 1..83160</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F For all n, a(n) >= A322586(n).

%o (PARI) A322585(n) = { my(f = factor(n)); for(i=1,#f~,if((primepi(f[i,1])!=i)||((i>1)&&(f[i-1,2]<f[i,2])),return(0))); (1); };

%Y Cf. A001221, A002110, A025487, A061395, A085089 (partial sums), A322584, A322586.

%K nonn

%O 1

%A _Antti Karttunen_, Dec 20 2018