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%I #6 Nov 21 2022 12:31:19
%S 1,1,1,1,-3,3,-3,5,-8,5,-11,36,-45,41,-72,142,-223,311,-493,851,-1243,
%T 1823,-3204,5336,-7906,12083,-20134,33133,-51685,81568,-133556,215363,
%U -340155,547916,-895895,1442323,-2300704,3718260,-6056908,9787064,-15755664,25541623
%N The inverse Euler transform of p(n) = n if n is prime, otherwise 1.
%C Conjecture: signum(a(n)) + (-1)^n = 0 for n >= 3.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler_transform</a>
%p # The function EulerInvTransform is defined in A358451.
%p a := EulerInvTransform(n -> ifelse(isprime(n), n, 1)):
%p seq(a(n), n = 0..41);
%p # Using EULERi the sequence is returned without a(0) and has offset 1.
%p f := n -> ifelse(isprime(n), n, 1): EULERi([seq(f(n), n = 1..41)]);
%Y Cf. A089026, A219224.
%K sign
%O 0,5
%A _Peter Luschny_, Nov 21 2022