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A322981 If n is the k-th prime power > 1, a(n) = k, otherwise a(n) = 0.

%I A322981 #14 Jun 17 2021 09:13:53
%S A322981 0,1,2,3,4,0,5,6,7,0,8,0,9,0,0,10,11,0,12,0,0,0,13,0,14,0,15,0,16,0,
%T A322981 17,18,0,0,0,0,19,0,0,0,20,0,21,0,0,0,22,0,23,0,0,0,24,0,0,0,0,0,25,0,
%U A322981 26,0,0,27,0,0,28,0,0,0,29,0,30,0,0,0,0,0,31,0,32,0,33,0,0,0,0,0,34,0,0,0,0,0,0,0,35
%N A322981 If n is the k-th prime power > 1, a(n) = k, otherwise a(n) = 0.
%C A322981 This is a ("corrected") variant of A095874, which uses the list of "powers of primes" A000961 instead of prime powers A246655. - _M. F. Hasler_, Jun 16 2021
%H A322981 Antti Karttunen, <a href="/A322981/b322981.txt">Table of n, a(n) for n = 1..16384</a>
%F A322981 a(n) = A010055(n) * A025528(n) = A069513(n) * A025528(n).
%F A322981 a(n) = A025528(A069513(n)*n), when assuming that A025528(0) = 0.
%F A322981 a(A000961(1+n)) = n for all n >= 1.
%o A322981 (PARI)
%o A322981 up_to = 16384;
%o A322981 A322981list(up_to) = { my(v=vector(up_to), k=0); for(n=1,up_to,if(isprimepower(n),k++; v[n] = k, v[n] = 0)); (v); };
%o A322981 v322981 = A322981list(up_to);
%o A322981 A322981(n) = v322981[n];
%o A322981 (PARI) A322981(n)=if(isprimepower(n),sum(i=1,exponent(n),primepi(sqrtnint(n,i)))) \\ _M. F. Hasler_, Jun 16 2021
%Y A322981 Cf. A000961 (powers of primes, including 1), A010055, A025528, A069513, A095874 (analog based on A000961), A246655 (prime powers > 1).
%Y A322981 Cf. A049084.
%K A322981 nonn
%O A322981 1,3
%A A322981 _Antti Karttunen_, Jan 01 2019