

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.


4



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
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OFFSET

1,1


LINKS



FORMULA



EXAMPLE

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


PROG

(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); };
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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



