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Number of primitive non-deficient numbers (A006039) dividing A337479(n).
4

%I #10 Oct 12 2020 20:36:31

%S 2,2,2,4,2,2,2,2,2,1,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,2,2,

%T 2,2,2,2,2,2,2,3,1,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,2,2,2,2,2,2,2,1,2,2,

%U 1,2,2,2,2,2,2,2,2,4,2,3,2,2,2,2,2,2,2,2,2,2,2,5,2,2,2,2,2,2,2,2,2,2,1,6,2

%N Number of primitive non-deficient numbers (A006039) dividing A337479(n).

%C The numbers in A337479 are those that become a primitive nondeficient number (term of A006039) when each of their prime factors is replaced by the next larger prime number.

%H Antti Karttunen, <a href="/A337539/b337539.txt">Table of n, a(n) for n = 1..24814</a>

%F a(n) = A337690(A337479(n)).

%e Table of n, A337479(n), a(n) and the relevant divisors starts:

%e n A337479(n) a(n) divisors in A006039

%e 1 120 2 6, 20;

%e 2 180 2 6, 20;

%e 3 300 2 6, 20;

%e 4 420 4 6, 20, 28, 70;

%e 5 504 2 6, 28;

%e 6 630 2 6, 70;

%e 7 660 2 6, 20;

%e 8 780 2 6, 20;

%e 9 924 2 6, 28;

%e 10 990 1 6;

%e 11 1020 2 6, 20;

%e 12 1050 2 6, 70;

%o (PARI)

%o isA071395(n) = if(sigma(n) <= 2*n, 0, fordiv(n, d, if((d != n)&&(sigma(d) >= 2*d), return(0))); (1)); \\ After code in A071395

%o isA006039(n) = ((sigma(n)==(2*n))||isA071395(n));

%o A337690(n) = sumdiv(n,d,isA006039(d));

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o isA337386(n) = { my(x=A003961(n)); (sigma(x)>=2*x); };

%o isA337479(n) = (isA337386(n)&&(1==sumdiv(n,d,isA337386(d))));

%o k=0; for(n=1,2^15,if(isA337479(n),k++; print1(A337690(n), ", ")));

%Y A006039, A337479 are used to define this sequence.

%Y See A000203 and A023196 for definitions of deficient and nondeficient.

%Y Subsequence of A337690.

%Y Cf. A337386.

%K nonn

%O 1,1

%A _Antti Karttunen_ and _Peter Munn_, Sep 20 2020