A045966 a(1)=3; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+2}^e_i.

3, 5, 7, 25, 11, 35, 13, 125, 49, 55, 17, 175, 19, 65, 77, 625, 23, 245, 29, 275, 91, 85, 31, 875, 121, 95, 343, 325, 37, 385, 41, 3125, 119, 115, 143, 1225, 43, 145, 133, 1375, 47, 455, 53, 425, 539, 155, 59, 4375, 169, 605, 161, 475, 61, 1715, 187, 1625, 203, 185, 67

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice

Comments

If we had a(1) = 1 (instead of 3), then this would be fully multiplicative with a(prime(k)) = prime(k+2) (see A357852). - Antti Karttunen, Jan 10 2020

References

• From a puzzle proposed by Marc LeBrun.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

See A027748, A124010 for factorization data for n.

Cf. A000040, A003961, A101300.

Sequences with similar definitions: A045967, A045968, A045970, A126272.

A059896 is used to express relationship between terms of this sequence.

A357852 is a slightly better version. - N. J. A. Sloane, Oct 29 2022

Programs

Haskell

a045966 1 = 3
a045966 n = product $ zipWith (^)
            (map a101300 $ a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Jun 03 2013, Dec 23 2011

Mathematica

a[1] = 3; a[n_] := With[{f = FactorInteger[n]}, Times @@ (Prime[PrimePi[f[[All, 1]]]+2]^f[[All, 2]])]; Array[a, 60] (* Jean-François Alcover, Jun 19 2015 *)

PARI

A045966(n) = if(1==n,3,my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(1+nextprime(1+f[i, 1]))); factorback(f)); \\ Antti Karttunen, Jan 10 2020

Formula

From Peter Munn, Dec 27 2019, for n >= 2, k >= 2: (Start)

a(n) = A003961^2(n).

a(n^k) = a(n)^k.

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

a(A059896(n,k)) = A059896(a(n), a(k)).

(End)

Extensions

More terms from David W. Wilson