A347047 Smallest squarefree semiprime whose prime indices sum to n.

6, 10, 14, 21, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514, 526

Offset: 3

Author

Gus Wiseman, Aug 22 2021

Keywords

• nonn

Comments

Compared to A001747, we have 21 instead of 22 and lack 2 and 4.

Compared to A100484 (shifted) we have 21 instead of 22 and lack 4.

Compared to A161344, we have 21 instead of 22 and lack 4 and 8.

Compared to A339114, we have 11 instead of 9 and lack 4.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

A squarefree semiprime (A006881) is a product of any two distinct prime numbers.

Examples

			The initial terms and their prime indices:
    6: {1,2}
   10: {1,3}
   14: {1,4}
   21: {2,4}
   26: {1,6}
   34: {1,7}
   38: {1,8}
   46: {1,9}
		

Crossrefs

The opposite version (greatest instead of smallest) is A332765.

These are the minima of rows of A338905.

The nonsquarefree version is A339114 (opposite: A339115).

A001358 lists semiprimes (squarefree: A006881).

A024697 adds up semiprimes by weight (squarefree: A025129).

A056239 adds up prime indices, row sums of A112798.

A246868 gives the greatest squarefree number whose prime indices sum to n.

A320655 counts factorizations into semiprimes (squarefree: A320656).

A338898, A338912, A338913 give the prime indices of semiprimes.

A338899, A270650, A270652 give the prime indices of squarefree semiprimes.

A339116 groups squarefree semiprimes by greater factor, sums A339194.

A339362 adds up prime indices of squarefree semiprimes.

Cf. A001221, A087112, A089994, A098350, A176504, A338900, A338901, A338904, A338907/A338908, A339005, A339191.

Programs

Mathematica

Table[Min@@Select[Table[Times@@Prime/@y,{y,IntegerPartitions[n,{2}]}],SquareFreeQ],{n,3,50}]

Python

from sympy import prime, sieve
def a(n):
    p = [0] + list(sieve.primerange(1, prime(n)+1))
    return min(p[i]*p[n-i] for i in range(1, (n+1)//2))
print([a(n) for n in range(3, 58)]) # Michael S. Branicky, Sep 05 2021