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

1,1

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.

Links

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

Formula

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

Example

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;

Prog

(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), ", ")));

Crossrefs

A006039, A337479 are used to define this sequence.

See A000203 and A023196 for definitions of deficient and nondeficient.

Subsequence of A337690.

Cf. A337386.

Sequence in context: A226534 A138260 A027389 * A111735 A211454 A242310

Adjacent sequences: A337536 A337537 A337538 * A337540 A337541 A337542

Keyword

nonn

Author

Antti Karttunen and Peter Munn, Sep 20 2020

Status

approved