A351099 Composite numbers k such that the maximal digit value in primorial base expansion of the arithmetic derivative of k is not larger than the maximal exponent in the prime factorization of k.

4, 8, 9, 10, 12, 14, 15, 16, 24, 25, 28, 30, 32, 36, 40, 45, 48, 49, 50, 54, 56, 58, 62, 64, 68, 74, 81, 87, 96, 98, 99, 108, 112, 120, 125, 128, 136, 155, 156, 160, 161, 162, 184, 189, 192, 196, 198, 203, 204, 208, 209, 210, 212, 217, 220, 221, 224, 225, 236, 244, 246, 247, 250, 252, 256, 268, 270, 272, 280, 282, 288

Offset: 1

Author

Antti Karttunen, Feb 03 2022

Keywords

• nonn

Comments

Composite k such that A328390(k) <= A051903(k).

Composite k for which A051903(A327859(n)) <= A051903(k).

Crossrefs

Cf. A003415, A051903, A276086, A327859, A328390, A351097, A351098 (subsequence).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
isA351099(n) = (n>1&&!isprime(n)&&(A328114(A003415(n)) <= A051903(n)));