A079168 Weighted quadratic roundness of n. If n=p_1^e_1...p^k_e^k, then a(n) = e_1 + (2^2 * e_2) + ... + (k^2 * e_k). Note that p_i<p_j, i<j, is assumed.

0, 1, 1, 2, 1, 5, 1, 3, 2, 5, 1, 6, 1, 5, 5, 4, 1, 9, 1, 6, 5, 5, 1, 7, 2, 5, 3, 6, 1, 14, 1, 5, 5, 5, 5, 10, 1, 5, 5, 7, 1, 14, 1, 6, 6, 5, 1, 8, 2, 9, 5, 6, 1, 13, 5, 7, 5, 5, 1, 15, 1, 5, 6, 6, 5, 14, 1, 6, 5, 14, 1, 11, 1, 5, 9, 6, 5, 14, 1, 8, 4, 5, 1, 15, 5, 5, 5, 7, 1, 18, 5, 6, 5, 5, 5, 9, 1, 9, 6, 10

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

a(1) = 0 (an empty sum).
a(10) = 5 as 10 = 2*5, therefore a(10) = (1^2)*1 + (2^2)*1 = 5
a(45) = 6 as 45 = 3^2 * 5, therefore a(45) = (1^2)*2 + (2^2)*1 = 6.
a(50) = 5 as 50 = 2^1 * 5^2, therefore a(50) = (1^2)*1 + (2^2)*2 = 9.
a(250) = 7 as 250 = 2^1 * 5^3, therefore a(250) = (1^2)*1 + (2^2)*3 = 13.

Prog

(PARI) weightedroundness2(n)=local(f, fl, s); f=factor(n); fl=length(f[, 1]); s=0; for (i=1, fl, s=s+i^2*f[, 2][i]); s alias(wr2, weightedroundness2) for (j=2, 500, print1(wr2(j)", "))

Crossrefs

Cf. A079167, A079169, A001222.

Sequence in context: A047818 A055972 A342414 * A332085 A055205 A342001

Adjacent sequences: A079165 A079166 A079167 * A079169 A079170 A079171

Keyword

nonn

Author

Jon Perry, Dec 31 2002

Extensions

a(1) = 0 prepended and more examples by Antti Karttunen, May 31 2017

Status

approved