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

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, 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, 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

Offset: 1

Author

Antti Karttunen and Peter Munn, Sep 20 2020

Keywords

• nonn

Comments

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.

Examples

			Table of n, A337479(n), a(n) and the relevant divisors starts:
   n   A337479(n)  a(n)  divisors in A006039
   1      120       2     6, 20;
   2      180       2     6, 20;
   3      300       2     6, 20;
   4      420       4     6, 20, 28, 70;
   5      504       2     6, 28;
   6      630       2     6, 70;
   7      660       2     6, 20;
   8      780       2     6, 20;
   9      924       2     6, 28;
  10      990       1     6;
  11     1020       2     6, 20;
  12     1050       2     6, 70;
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..24814

Crossrefs

A006039, A337479 are used to define this sequence.

See A000203 and A023196 for definitions of deficient and nondeficient.

Subsequence of A337690.

Cf. A337386.

Programs

PARI

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
isA006039(n) = ((sigma(n)==(2*n))||isA071395(n));
A337690(n) = sumdiv(n,d,isA006039(d));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA337386(n) = { my(x=A003961(n)); (sigma(x)>=2*x); };
isA337479(n) = (isA337386(n)&&(1==sumdiv(n,d,isA337386(d))));
k=0; for(n=1,2^15,if(isA337479(n),k++; print1(A337690(n), ", ")));

Formula

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