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.

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

Author

Antti Karttunen, Jan 31 2024

Keywords

• nonn

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, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2450
• Index entries for sequences related to primorial base

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.

Programs

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));