A324910 -id:A324910 - cp's OEIS frontend

A324911 Multiplicative with a(p^e) = A156552(p^e).

1, 1, 2, 3, 4, 2, 8, 7, 6, 4, 16, 6, 32, 8, 8, 15, 64, 6, 128, 12, 16, 16, 256, 14, 12, 32, 14, 24, 512, 8, 1024, 31, 32, 64, 32, 18, 2048, 128, 64, 28, 4096, 16, 8192, 48, 24, 256, 16384, 30, 24, 12, 128, 96, 32768, 14, 64, 56, 256, 512, 65536, 24, 131072, 1024, 48, 63, 128, 32, 262144, 192, 512, 32, 524288, 42, 1048576, 2048, 24, 384

Offset: 1

Antti Karttunen, Apr 14 2019

			For n = 900 = 2^2 * 3^2 * 5^2, a(900) = A156552(4) * A156552(9) * A156552(25) = 3*6*12 = 216.

Cf. A156552, A324910, A324912.

Cf. also A324106.

A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res }; \\ From A156552
A324911(n) = { my(f=factor(n)); prod(i=1, #f~, A156552(f[i,1]^f[i,2])); };

A328892 If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 3, 1, 2, 2, 8, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 4, 3, 1, 3, 1, 16, 2, 2, 2, 4, 1, 2, 2, 5, 1, 3, 1, 3, 3, 2, 1, 9, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 4, 1, 2, 3, 32, 2, 3, 1, 3, 2, 3, 1, 6, 1, 2, 3, 3, 2, 3, 1, 9, 8, 2, 1, 4, 2, 2, 2, 5, 1, 4

Offset: 1

Ilya Gutkovskiy, Oct 29 2019

nonn

			a(72) = 6 because 72 = 2^3 * 3^2 and 2^(3 - 1) + 2^(2 - 1) = 6.

Index entries for sequences computed from exponents in factorization of n

Cf. A000040 (positions of 1's), A008481, A011782, A162510, A324910.

a:= n-> add(2^(i[2]-1), i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 29 2019

a[1] = 0; a[n_] := Plus @@ (2^(#[[2]] - 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 90}]

a(n)={vecsum([2^(k-1) | k<-factor(n)[,2]])} \\ Andrew Howroyd, Oct 29 2019

If n = Product (p_j^k_j) then a(n) = Sum ordered partition(k_j).

Additive with a(p^e) = 2^(e-1).

cp's OEIS Frontend

A324911 Multiplicative with a(p^e) = A156552(p^e).

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