A358674 Numbers k for which there is a factorization of k into such a pair of natural numbers x and y, that the sum (x * y') + (x' * y) will generate at least one carry when the addition is done in the primorial base. Here n' stands for A003415(n), the arithmetic derivative of n.

8, 9, 10, 15, 16, 20, 21, 22, 24, 25, 28, 30, 32, 33, 34, 35, 36, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 64, 65, 66, 68, 69, 72, 75, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 118, 119

Offset

1,1

Links

Table of n, a(n) for n=1..73.

Index entries for sequences related to primorial base

Formula

{k | A358235(k) < A038548(k)}.

Example

Refer to the examples in A358235 to see why 24 is included in this sequence.

Prog

(PARI) isA358674(n) = !A358672(n);
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
A329041sq(row, col) = A327936(A276086(row)*A276086(col));
isA358674(n) = { fordiv(n, d, if(d>(n/d), return(0)); if(1<A329041sq((d*A003415(n/d)), (A003415(d)*(n/d))), return(1))); (0); };

Crossrefs

Positions of zeros in A358672.

Cf. A003415, A038548, A276086, A329041, A358235, A358673 (complement).

Subsequences: A016754 (without its initial 1), A358675.

Sequence in context: A374122 A072381 A046415 * A358675 A091417 A069237

Adjacent sequences: A358671 A358672 A358673 * A358675 A358676 A358677

Keyword

nonn,base

Author

Antti Karttunen, Nov 26 2022

Status

approved