A336845 a(n) = A000005(n) * A003961(n), where A003961 is the prime shift towards larger primes, and A000005 gives the number of divisors of n, and also of A003961(n).

1, 6, 10, 27, 14, 60, 22, 108, 75, 84, 26, 270, 34, 132, 140, 405, 38, 450, 46, 378, 220, 156, 58, 1080, 147, 204, 500, 594, 62, 840, 74, 1458, 260, 228, 308, 2025, 82, 276, 340, 1512, 86, 1320, 94, 702, 1050, 348, 106, 4050, 363, 882, 380, 918, 118, 3000, 364, 2376, 460, 372, 122, 3780, 134, 444, 1650, 5103, 476, 1560

Offset

1,2

Comments

Dirichlet convolution of A003961 with itself.

Sequence is not injective, as it has duplicate values, for example: a(162) = a(243) = 18750. See also comments in A336475.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Formula

Multiplicative with a(prime(i)^e) = (e+1) * prime(1+i)^e.

a(n) = A000005(n) * A003961(n).

a(n) = A038040(A003961(n)).

a(n) = A336841(n) + A003973(n).

a(n) is odd if and only if n is a square.

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336845(n) = (numdiv(n)*A003961(n))
(PARI) A336845(n) = { my(f = factor(n)); prod(i=1, #f~, (1+f[i, 2]) * (nextprime(1+f[i, 1])^f[i, 2])); };
(PARI) A336845(n) = sumdiv(n, d, A003961(d)*A003961(n/d));

Crossrefs

Cf. A000005, A000203, A000290, A003961, A038040, A336475.

Cf. also A336841, A336846 [= gcd(a(n),A003973(n))], A336847, A336848.

Sequence in context: A323107 A077621 A298736 * A324617 A359145 A287989

Adjacent sequences: A336842 A336843 A336844 * A336846 A336847 A336848

Keyword

nonn,mult

Author

Antti Karttunen, Aug 06 2020

Status

approved