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A283980 a(n) = A003961(n)*A006519(n). 13
1, 6, 5, 36, 7, 30, 11, 216, 25, 42, 13, 180, 17, 66, 35, 1296, 19, 150, 23, 252, 55, 78, 29, 1080, 49, 102, 125, 396, 31, 210, 37, 7776, 65, 114, 77, 900, 41, 138, 85, 1512, 43, 330, 47, 468, 175, 174, 53, 6480, 121, 294, 95, 612, 59, 750, 91, 2376, 115, 186, 61, 1260, 67, 222, 275, 46656, 119, 390, 71, 684, 145, 462, 73, 5400, 79, 246, 245 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Completely multiplicative since both A003961 and A006519 are. - Andrew Howroyd, Jul 25 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10001

FORMULA

a(n) = A003961(n)*A006519(n).

From Michael De Vlieger, Dec 29 2019: (Start)

a(p_k) = p_(k+1) for odd prime p.

a(2^k) = 6^k.

a(p_k#) = p_(k+1)# for p_k# = A002110(k). (End)

EXAMPLE

From Michael De Vlieger, Dec 29 2019: (Start)

a(1) = 1 since 1 is the empty product.

a(2) = 6 because 2 = 2^1 in form p_k^e; switching p_(k+1) for p, we have 3^1 = 3, and the largest power of 2 dividing 2 is 2^1 = 2; thus 3 * 2 = 6.

a(4) = 36 since 4 = 2^2 -> 4(3^2).

a(6) = 30 since 6 = 2^1 * 3^1 -> 2(3 * 5).

a(12) = 180 since 12 = 2^2 * 3 -> 4(3^2 * 5) = 4(45) = 180.

a(30) = 210 since 30 = 2 * 3 * 5 -> 2(3 * 5 * 7) = 210.

(End)

MATHEMATICA

Array[(Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2] &, 75] (* Michael De Vlieger, Dec 29 2019 *)

PROG

(Scheme) (define (A283980 n) (* (A006519 n) (A003961 n)))

(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)} \\ Andrew Howroyd, Jul 25 2018

CROSSREFS

Cf. A003961, A006519, A283477.

Sequence in context: A070399 A137763 A029763 * A288211 A038259 A302750

Adjacent sequences:  A283977 A283978 A283979 * A283981 A283982 A283983

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Mar 19 2017

STATUS

approved

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Last modified August 3 19:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)