A394500 Ways to represent n = k + p where p is prime and k > 0 is not squarefree.

0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 3, 1, 1, 2, 3, 1, 2, 1, 3, 2, 4, 2, 5, 0, 4, 2, 6, 2, 5, 3, 6, 3, 4, 2, 7, 1, 5, 4, 6, 2, 6, 2, 6, 2, 6, 3, 9, 2, 7, 4, 9, 4, 7, 3, 10, 6, 9, 3, 10, 1, 10, 5, 10, 2, 11, 4, 11, 6, 9, 4, 12, 2, 10, 4, 11, 3, 12, 4, 13, 5, 10, 5

Offset

1,11

Links

Table of n, a(n) for n=1..82.

Ethan S. Lee and Rowan O'Clarey, On the Sum of a Prime and a Number that is not Square-Free, arXiv preprint (2026). arXiv:2605.02426 [math.NT]

Formula

Lee & O'Clarey prove that a(n) > 0 for large enough n and conjecture that a(n) > 0 for n > 24.

Prog

(PARI) a(n)=my(s); forfactored(k=4, n-2, if(issquarefree(k), next); if(isprime(n-k[1]), s++)); s \\ Charles R Greathouse IV, May 24 2026

Crossrefs

Sequence in context: A016464 A245570 A243925 * A348282 A030727 A278564

Adjacent sequences: A394497 A394498 A394499 * A394502 A394503 A394504

Keyword

nonn

Author

Charles R Greathouse IV, May 24 2026

Status

approved