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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).
7
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.
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. also A336841, A336846 [= gcd(a(n),A003973(n))], A336847, A336848.
Sequence in context: A323107 A077621 A298736 * A324617 A359145 A287989
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Aug 06 2020
STATUS
approved