A336561 Numbers k at which point A336459(k) appears multiplicative, but A051027(k) does not.

506, 1819, 2024, 2714, 3674, 3818, 4554, 5088, 5750, 5786, 6026, 6762, 6842, 7215, 7276, 9487, 9523, 10442, 11895, 12397, 12650, 13178, 13303, 14235, 14696, 15272, 15962, 16346, 16371, 18216, 18458, 19274, 19514, 19690, 19706, 20179, 20378, 21079, 21255, 21626, 22066, 22586, 22682, 23000, 23144, 23322, 24104, 24246

Offset: 1

Author

Antti Karttunen, Jul 25 2020

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11481
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A051027, A065330, A336459.

Cf. also A336549.

Subsequence of A336548, and probably also of A336560.

Programs

PARI

is_fun_mult_on_n(fun,n) = { my(f=factor(n)); prod(k=1,#f~,fun(f[k,1]^f[k,2]))==fun(n); };
A051027(n) = sigma(sigma(n));
A336546(n) = is_fun_mult_on_n(A051027,n);
A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));
A336459(n) = A065330(A051027(n));
isA336561(n) = (A336546(n)A336459,n));