A120119 Multiplicative function from integers to sums of two squares.

1, 2, 5, 4, 9, 10, 13, 8, 25, 18, 17, 20, 29, 26, 45, 16, 37, 50, 41, 36, 65, 34, 49, 40, 81, 58, 125, 52, 53, 90, 61, 32, 85, 74, 117, 100, 73, 82, 145, 72, 89, 130, 97, 68, 225, 98, 101, 80, 169, 162, 185, 116, 109, 250, 153, 104, 205, 106, 113, 180, 121, 122, 325, 64

Offset

1,2

Comments

The values here are a rearrangement of A001481. The numbers in A001481 have unique factorization (with factors restricted to A001481), with the numbers in A055025 being the "primes".

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

Totally multiplicative with a(prime(k)) = A055025(k).

Prog

(PARI) isA055025(n)=(isprime(n) && n%4<3) || (issquare(n, &n) && isprime(n) && n%4==3);
a(n)={if(n==1, 1, my(f=factor(n), m=primepi(vecmax(f[, 1])), L=List(), k=1); while(#L<m, k++; if(isA055025(k), listput(L, k))); prod(i=1, #f~, L[primepi(f[i, 1])]^f[i, 2]))} \\ Andrew Howroyd, Dec 22 2025

Crossrefs

Cf. A001481, A055025, A000040.

Sequence in context: A227368 A339597 A368736 * A364035 A298011 A048678

Adjacent sequences: A120116 A120117 A120118 * A120120 A120121 A120122

Keyword

mult,easy,nonn

Author

Franklin T. Adams-Watters, Aug 15 2006

Status

approved