A166651 -id:A166651 - cp's OEIS frontend

A319525 Completely multiplicative with a(prime(k)) = prime(2*k - 1) (where prime(k) denotes the k-th prime).

1, 2, 5, 4, 11, 10, 17, 8, 25, 22, 23, 20, 31, 34, 55, 16, 41, 50, 47, 44, 85, 46, 59, 40, 121, 62, 125, 68, 67, 110, 73, 32, 115, 82, 187, 100, 83, 94, 155, 88, 97, 170, 103, 92, 275, 118, 109, 80, 289, 242, 205, 124, 127, 250, 253, 136, 235, 134, 137, 220

Offset: 1

Rémy Sigrist, Sep 22 2018

This sequence is a permutation of A066208.

See A297002 for a similar sequence.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences computed from indices in prime factorization

Cf. A000079, A066208, A297002.

Cf. also A166651.

a(n) = my (f=factor(n)); prod(i=1, #f~, prime(2*primepi(f[i, 1]) - 1)^f[i, 2])

a(n) = A064989(A297002(n)).

a(n) >= n with equality iff n is a power of 2 (A000079).

A167330 Totally multiplicative sequence with a(p) = 2*(2p-1) = 4p-2 for prime p.

Original entry on oeis.org

1, 6, 10, 36, 18, 60, 26, 216, 100, 108, 42, 360, 50, 156, 180, 1296, 66, 600, 74, 648, 260, 252, 90, 2160, 324, 300, 1000, 936, 114, 1080, 122, 7776, 420, 396, 468, 3600, 146, 444, 500, 3888, 162, 1560, 170, 1512, 1800, 540, 186, 12960, 676, 1944

Offset: 1

Jaroslav Krizek, Nov 01 2009

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001222, A061142, A166651.

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((2*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (4*p-2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

a(n) = {my(f=factor(n)); for (k=1, #f~, f[k,1] = 4*f[k,1]-2;); factorback(f);} \\ Michel Marcus, Jun 06 2016

Multiplicative with a(p^e) = (2*(2p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(2*p(k)-1))^e(k).

a(n) = A061142(n) * A166651(n) = 2^bigomega(n) * A166651(n) = 2^A001222(n) * A166651(n).

cp's OEIS Frontend

A319525 Completely multiplicative with a(prime(k)) = prime(2*k - 1) (where prime(k) denotes the k-th prime).

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