A073322 -id:A073322 - cp's OEIS frontend

A072548 a(n) = sigma(n) mod PrimePi(n).

0, 0, 1, 0, 0, 0, 3, 1, 2, 2, 3, 2, 0, 0, 1, 4, 4, 4, 2, 0, 4, 6, 6, 4, 6, 4, 2, 0, 2, 10, 8, 4, 10, 4, 3, 2, 0, 8, 6, 3, 5, 2, 0, 8, 2, 3, 4, 12, 3, 12, 8, 6, 8, 8, 8, 0, 10, 9, 15, 8, 6, 14, 1, 12, 0, 11, 12, 1, 11, 12, 15, 11, 9, 19, 14, 12, 0, 14, 10, 11, 16, 15, 17, 16, 17, 5, 19, 18, 18

Offset: 2

Labos Elemer, Aug 05 2002

nonn

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Cf. A000203, A000720, A073321, A073322, A073323, A073324.

[SumOfDivisors(n) mod (#PrimesUpTo(n)): n in [2..100]]; // Vincenzo Librandi, Dec 10 2018

with(numtheory): seq(modp(sigma(n),pi(n)),n=2..100); # Muniru A Asiru, Dec 10 2018

Table[Mod[DivisorSigma[1, w], PrimePi[w]], {w, 1, 128}]

a(n) = sigma(n) % primepi(n); \\ Michel Marcus, Dec 10 2018

a(n) = A000203(n) mod A000720(n).

A073323 Smallest k such that A073259(k)=n or 0 if there is no such value; the first number of which length of fixed-point-list terminated by k-th composite number equals n.

Original entry on oeis.org

0, 0, 4, 1, 29, 153, 4913, 73114, 1985627, 69912446, 2734947158

Offset: 1

Labos Elemer, Jul 29 2002

Occurrences of lengths [1-10] for n<=10000000 are {0,0,64,4662,310495,6468633,3041909,173579,658,0}.

			For lengths n=3, 4, 5, 6, 7, 8 the corresponding lists are: {4, 7, 9}, {1, 2, 3, 4}, {29, 40, 42, 43, 44}, {153, 190, 196, 198, 199, 200}, {4913, 5570, 5649, 5656, 5658, 5659, 5660} and {73114, 80343, 80982, 81039, 81046, 81048, 81049, 81050}.

Cf. A002808, A073259, A073320-A073322.

lfp[x_] := Length[FixedPointList[x + PrimePi[ # ] + 1 &, x]]-1 t=Table[0, {15}]; Do[s=lfp[n]; If[s<16&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t

a(n) = Min{k: A073259(k)=n}

a(10)-a(11) from Sean A. Irvine, Nov 22 2024

cp's OEIS Frontend

A072548 a(n) = sigma(n) mod PrimePi(n).

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