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A369639
Numbers k, not squarefree, such that the maximal digit in the primorial base representation of k' is <= 3, where k' stands for the arithmetic derivative of k, A003415.
3
4, 8, 9, 12, 16, 18, 24, 25, 28, 32, 36, 40, 44, 45, 48, 49, 50, 54, 56, 60, 63, 68, 76, 81, 92, 96, 98, 99, 108, 112, 120, 121, 125, 136, 147, 153, 156, 160, 175, 184, 189, 192, 196, 198, 204, 208, 212, 220, 225, 228, 234, 236, 244, 250, 252, 268, 270, 280, 284, 289, 296, 300, 315, 316, 328, 333, 338, 340, 344, 361
OFFSET
1,1
COMMENTS
Nonsquarefree numbers k (A013929) such that A327859(k) = A276086(A003415(k)) is biquadratefree number (A046100), or equally that A328114(A003415(k)) <= 3.
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); };
isA369639(n) = (n>0 && !issquarefree(n) && ismaxprimobasedigit_at_most(A003415(n), 3));
CROSSREFS
Nonsquarefree terms of A369642 form a subsequence.
Sequence in context: A359869 A034030 A057109 * A069189 A375399 A371601
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 01 2024
STATUS
approved