A072548 -id:A072548 - cp's OEIS frontend

A073722 Least k such that sigma(k) mod primepi(k) = n or zero if no such number exists.

2, 4, 10, 8, 17, 42, 23, 111, 32, 59, 31, 67, 49, 110, 63, 60, 82, 84, 89, 75, 191, 98, 141, 97, 101, 256, 171, 169, 148, 144, 140, 159, 143, 222, 220, 172, 206, 2124, 183, 315, 263, 567, 201, 358, 204, 470, 243, 391, 264, 563, 295, 382, 290, 285, 313, 324, 307

Offset: 0

Labos Elemer, Aug 05 2002

nonn

			n=8: a(8)=32 since sigma(32)=63, primepi(32)=11, and 63 mod 11 = 8.

Sean A. Irvine, Table of n, a(n) for n = 0..10000

Cf. A000203, A000720, A072548, A073721-A073724.

t=Table[0, {100}]; Do[s=Mod[DivisorSigma[1, n], PrimePi[n]]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 2, 10000}]; t

a(n) = min{x: A000203(x) mod A000720(x) = n}.

a(0)=2 inserted by Sean A. Irvine, Dec 16 2024

A073723 Numbers k such that sigma(k) mod pi(k) = 1.

Original entry on oeis.org

4, 9, 16, 64, 69, 218, 592, 808, 910, 1921, 1957, 2648, 2860, 7609, 13462, 14953, 16838, 20688, 27050, 44471, 80440, 91860, 122351, 131095, 154606, 166121, 171396, 226831, 257467, 318016, 614626, 726560, 1225277, 1366686, 1465910, 1508284, 1790754, 1816934, 1873100

Offset: 1

Labos Elemer, Aug 05 2002

nonn

Amiram Eldar, Table of n, a(n) for n = 1..100

Cf. A000203 (sigma), A000720 (pi), A072548.

Do[s=Mod[DivisorSigma[1, n], PrimePi[n]]; If[s==1, Print[n]], {n, 1, 1000000}]

isok(k) = k > 1 && sigma(k) % primepi(k) == 1 \\ Andrew Howroyd, Dec 12 2024

list(lim) = {my(i = 1, p = 2); forprime(q = 3, lim, for(k = p, q-1, if(sigma(k) % i == 1, print1(k, ", "))); i++; p = q);} \\ Amiram Eldar, Mar 18 2025

More terms from Amiram Eldar, Mar 18 2025

cp's OEIS Frontend

A073722 Least k such that sigma(k) mod primepi(k) = n or zero if no such number exists.

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