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A141676 Numbers n such that: mod(sigma_0(n)*PrimePi(n), 8) = 0. 1
1, 7, 8, 10, 14, 15, 19, 20, 21, 22, 24, 30, 37, 38, 39, 40, 42, 46, 53, 54, 55, 56, 57, 58, 62, 65, 66, 70, 71, 72, 78, 82, 88, 89, 90, 91, 92, 93, 94, 95, 96, 102, 104, 105, 107, 108, 110, 114, 115, 118, 119, 120, 122, 123, 125, 126, 128, 130, 131, 132, 133, 134, 135 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Nearly half of all integers fall in this category.

mod(sigma_0(n)*PrimePi(n), 8) == 4 is the next biggest category.

While plotting sigma_0(n)*PrimePi(n) it was noticed that this product gives a plot with nearly 8 line levels.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = mod(sigma_0(n)*PrimePi(n), 8) = 0.

MATHEMATICA

Flatten[Table[If[Mod[DivisorSigma[0, n]*PrimePi[n], 8] == 0, n, {}], {n, 1, 200}]]

PROG

(PARI) for(n=1, 150, if(Mod(sigma(n, 0)*primepi(n), 8)==0, print1(n", "))) \\ G. C. Greubel, Apr 02 2019

(MAGMA) [n: n in [1..150] | NumberOfDivisors(n)*#PrimesUpTo(n) mod 8 eq 0 ]; // G. C. Greubel, Apr 02 2019

(Sage) [n for n in (1..150) if mod(sigma(n, 0)*prime_pi(n), 8)==0 ] # G. C. Greubel, Apr 02 2019

CROSSREFS

Cf. A000005 (sigma_0), A000720 (PrimePi).

Sequence in context: A080113 A243078 A048588 * A127164 A153972 A286420

Adjacent sequences:  A141673 A141674 A141675 * A141677 A141678 A141679

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Sep 07 2008

EXTENSIONS

Edited by G. C. Greubel, Apr 02 2019

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)