A336561 - OEIS

%I #8 Jul 26 2020 09:51:21

%S 506,1819,2024,2714,3674,3818,4554,5088,5750,5786,6026,6762,6842,7215,

%T 7276,9487,9523,10442,11895,12397,12650,13178,13303,14235,14696,15272,

%U 15962,16346,16371,18216,18458,19274,19514,19690,19706,20179,20378,21079,21255,21626,22066,22586,22682,23000,23144,23322,24104,24246

%N Numbers k at which point A336459(k) appears multiplicative, but A051027(k) does not.

%H Antti Karttunen, <a href="/A336561/b336561.txt">Table of n, a(n) for n = 1..11481</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e 506 = 2*11*23 is a term as A336459(2)*A336459(11)*A336459(23) = 1*7*5 = 35 = A336459(506), while A051027(2)*A051027(11)*A051027(23) = 4*28*60 = 6720 <> A051027(506) = 2520. Note that 2520 = 2^3 * 3^2 * 5 * 7, thus A065330(2520) = 5*7 = 35.

%o (PARI)

%o is_fun_mult_on_n(fun,n) = { my(f=factor(n)); prod(k=1,#f~,fun(f[k,1]^f[k,2]))==fun(n); };

%o A051027(n) = sigma(sigma(n));

%o A336546(n) = is_fun_mult_on_n(A051027,n);

%o A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));

%o A336459(n) = A065330(A051027(n));

%o isA336561(n) = (A336546(n)<is_fun_mult_on_n(A336459,n));

%Y Cf. A051027, A065330, A336459.

%Y Cf. also A336549.

%Y Subsequence of A336548, and probably also of A336560.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jul 25 2020