A336560 - OEIS

A336560

Numbers k at which points A336456(k) appears multiplicative, but A051027(k) does not.

15, 39, 51, 60, 78, 87, 95, 111, 123, 143, 159, 183, 204, 215, 219, 222, 231, 240, 247, 267, 291, 303, 312, 323, 327, 330, 335, 339, 348, 366, 380, 399, 407, 411, 438, 444, 447, 455, 471, 494, 506, 519, 543, 559, 579, 582, 591, 624, 636, 654, 671, 687, 695, 699, 703, 714, 723, 731, 732, 767, 771, 779, 798, 803, 807

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OFFSET

1,1

COMMENTS

Numbers in A336557 but not in A336547.

Note that if A051027(k) = Product_{p^e|k} A051027(p^e) then also A336456(n) = Product_{p^e|n} A336456(p^e), because A336456(n) = A335915(A051027(n)) and A335915 is fully multiplicative, thus A336547 is a subsequence of A336557.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..25000

PROG

(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));

A000265(n) = (n>>valuation(n, 2));

A335915(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265((f[k, 1]^2)-1)^f[k, 2]))); };

A336456(n) = A335915(A051027(n));

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

A336556(n) = is_fun_mult_on_n(A336456, n);

isA336560(n) = (A336546(n)<A336556(n));