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A337539 Number of primitive non-deficient numbers (A006039) dividing A337479(n).

%I A337539 #10 Oct 12 2020 20:36:31
%S A337539 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 A337539 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 A337539 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 A337539 Number of primitive non-deficient numbers (A006039) dividing A337479(n).
%C A337539 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 A337539 Antti Karttunen, <a href="/A337539/b337539.txt">Table of n, a(n) for n = 1..24814</a>
%F A337539 a(n) = A337690(A337479(n)).
%e A337539 Table of n, A337479(n), a(n) and the relevant divisors starts:
%e A337539    n   A337479(n)  a(n)  divisors in A006039
%e A337539    1      120       2     6, 20;
%e A337539    2      180       2     6, 20;
%e A337539    3      300       2     6, 20;
%e A337539    4      420       4     6, 20, 28, 70;
%e A337539    5      504       2     6, 28;
%e A337539    6      630       2     6, 70;
%e A337539    7      660       2     6, 20;
%e A337539    8      780       2     6, 20;
%e A337539    9      924       2     6, 28;
%e A337539   10      990       1     6;
%e A337539   11     1020       2     6, 20;
%e A337539   12     1050       2     6, 70;
%o A337539 (PARI)
%o A337539 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 A337539 isA006039(n) = ((sigma(n)==(2*n))||isA071395(n));
%o A337539 A337690(n) = sumdiv(n,d,isA006039(d));
%o A337539 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A337539 isA337386(n) = { my(x=A003961(n)); (sigma(x)>=2*x); };
%o A337539 isA337479(n) = (isA337386(n)&&(1==sumdiv(n,d,isA337386(d))));
%o A337539 k=0; for(n=1,2^15,if(isA337479(n),k++; print1(A337690(n), ", ")));
%Y A337539 A006039, A337479 are used to define this sequence.
%Y A337539 See A000203 and A023196 for definitions of deficient and nondeficient.
%Y A337539 Subsequence of A337690.
%Y A337539 Cf. A337386.
%K A337539 nonn
%O A337539 1,1
%A A337539 _Antti Karttunen_ and _Peter Munn_, Sep 20 2020