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A369642
Composite numbers k, not squarefree semiprimes, such that k' is a sum of distinct primorial numbers, where k' stands for the arithmetic derivative of k, A003415.
5
9, 16, 28, 30, 45, 108, 112, 136, 189, 198, 210, 212, 225, 236, 244, 246, 282, 290, 361, 374, 399, 435, 507, 1480, 1940, 2132, 2212, 2308, 2356, 2524, 2655, 2766, 2802, 3018, 3054, 3501, 3590, 3771, 3938, 4225, 4454, 4755, 4809, 5005, 5763, 6123, 6771, 9024, 9936, 10295, 11881, 12221, 16296, 22491, 24389, 26865
OFFSET
1,1
COMMENTS
Composite numbers k, not squarefree semiprimes, such that A327859(k) = A276086(A003415(k)) is squarefree number, or equally, k' is in A276156.
Squares that appear in this sequence: 9, 16, 225, 361, 4225, 11881, 1371241, 1635841, 225930961, 228644641, 229189321, 262083721, ...
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
ismaxprimobasedigit_at_most(n, k) = { my(s=0, p=2); while(n, if((n%p)>k, return(0)); n = n\p; p = nextprime(1+p)); (1); };
A369640(n) = if(n<2 || isprime(n), 0, ismaxprimobasedigit_at_most(A003415(n), 1));
isA369642(n) = (((bigomega(n)>2)||(bigomega(n)>omega(n))) && A369640(n));
CROSSREFS
Sequence A369641 without any terms of A006881.
Cf. A003415, A276086, A276156, A327859, A369647 (subsequence after its two initial terms).
Nonsquarefree terms all occur in A369639.
Sequence in context: A303873 A257496 A351435 * A162616 A153362 A039788
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 31 2024
STATUS
approved