OFFSET
1,2
COMMENTS
Intersection with A048103 gives the fixed points (1, 2, 10, 15, 5005, ...) of A327859. Question: Does that set preclude nonsquarefree numbers? Certainly it does not contain any multiples of 9. See also comments in A328110.
If k == 2 (mod 4), then both A003415(k) and A276085(k) are odd, and the latter is of the form 4m+1 (if k has an odd number of prime factors), or of the form 4m+3 (if k has an even number of prime factors). Therefore, for k of the form 4m+2 to be included in this sequence, a necessary condition is that it must be either in the intersection of A026424 and A358772 (like, for example, 2 is) or in A369668 (the intersection of A028260 and A358774), like for example, 10 is.
If k is odd, then A276085(k) is even, and for A003415(k) to be even with k odd, then k has to be in A046337 (odd numbers with an even number of prime factors, counted with multiplicity). But A276085(A046337(n)) == 0 (mod 4) for all n, so also A003415(k) has to be a multiple of 4, so k has to be in A360110 (itself a subsequence of A369002), like for example k=15 and k=5005 are.
If it exists, a(7) > 2^19.
EXAMPLE
PROG
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Feb 05 2024
STATUS
approved