A304776 - OEIS

A304776

A weakening function. a(n) = n / A007947(n)^(A051904(n) - 1) where A007947 is squarefree kernel and A051904 is minimum prime exponent.

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20, 21, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 2, 65, 66, 67, 68, 69, 70, 71, 12, 73, 74, 75, 76, 77, 78, 79, 80, 3, 82, 83

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This function takes powerful numbers (A001694) to weak numbers (A052485) and leaves weak numbers unchanged.

First differs from A052410 at a(72) = 12, A052410(72) = 72.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = n / A354090(n). - Antti Karttunen, May 19 2022

Sum_{k=1..n} a(k) ~ n^2 / 2. - Amiram Eldar, Sep 12 2024

MATHEMATICA

spr[n_]:=Module[{f, m}, f=FactorInteger[n]; m=Min[Last/@f]; n/Times@@First/@f^(m-1)];

Array[spr, 100]

PROG

(PARI)

A007947(n) = factorback(factorint(n)[, 1]);

A051904(n) = if((1==n), 0, vecmin(factor(n)[, 2]));

A304776(n) = (n/(A007947(n)^(A051904(n)-1))); \\ Antti Karttunen, May 19 2022

(PARI) a(n) = if(n == 1, 1, my(f = factor(n), p = f[, 1], e = f[, 2]); n / vecprod(p)^(vecmin(e) - 1)); \\ Amiram Eldar, Sep 12 2024

CROSSREFS

Cf. A001597, A001694, A005117, A007947, A013929, A047966, A051903, A051904, A052485, A062759, A066636, A066638, A072774, A304768, A354090.

Sequence in context: A166140 A019555 A243074 * A052410 A327501 A175781

Adjacent sequences: A304773 A304774 A304775 * A304777 A304778 A304779

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 18 2018

EXTENSIONS

Data section extended up to a(83) by Antti Karttunen, May 19 2022

STATUS

approved