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%I #9 Apr 05 2021 21:35:13
%S 1,2,5,4,11,30,17,8,25,110,23,60,31,238,385,16,41,150,47,220,935,506,
%T 59,120,121,806,125,476,67,2310,73,32,1495,1394,2431,900,83,1786,2635,
%U 440,97,39270,103,1012,1925,2714,109,240,289,1210,3895,1612,127,750
%N a(n) = A343033(n, n).
%C This sequence has similarities with A087019.
%H Rémy Sigrist, <a href="/A343035/b343035.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%F a(n) = n iff n is a power of 2 (A000079).
%F a(prime(i)^k) = prime(2*i-1)^k for any i > 0 and k > 0.
%e For n = 40:
%e - 40 = 5 * 2^3, so:
%e (11 7 5 3 2)
%e 1 0 3
%e x 1 0 3
%e -------
%e 1 0 3
%e 0 0 0
%e + 1 0 1
%e -----------
%e 1 0 1 0 3,
%e - hence a(40) = 11 * 5 * 2^3 = 440.
%o (PARI) a(n) = { my (r=1, pp=factor(n)[, 1]~); for (i=1, #pp, for (j=1, #pp, my (p=prime(primepi(pp[i])+primepi(pp[j])-1), v=valuation(r, p), w=min(valuation(n, pp[i]), valuation(n, pp[j]))); if (w>v, r*=p^(w-v)))); r }
%Y Cf. A000079, A087019, A343033.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Apr 03 2021
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