A063071 - OEIS

A063071

Numbers k such that sigma(k)*omega(k) = sigma(k+1)*omega(k+1), where omega(k) is the number of distinct prime divisors of n (A001221).

14, 206, 1334, 1634, 2685, 14841, 18873, 19358, 26872, 33998, 36566, 42818, 56564, 84134, 116937, 122073, 161001, 162602, 166934, 174717, 190773, 193893, 239499, 245768, 260096, 289454, 326884, 383594, 409695, 422073, 430137, 438993, 440013

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

OFFSET

1,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 100 terms from Harry J. Smith)

EXAMPLE

The function b(n) = sigma(n)*omega(n) starts 0, 3, 4, 7, 6, 24, 8, 15, 13, 36, 12, 56, 14, 48, 48, 31, 18,.. at n>=1. b(14)=b(15)=48 are the same values, so 14 is in the sequence. - R. J. Mathar, Jul 19 2026

MATHEMATICA

Select[Range[5000], PrimeNu[#]*DivisorSigma[1, #] == PrimeNu[# + 1]*DivisorSigma[1, # + 1] &] (* G. C. Greubel, Apr 23 2017 *)

PROG

(PARI) for(n=1, 10^6, if(sigma(n)*omega(n)==sigma(n+1)*omega(n+1), print(n)))

(PARI) { n=0; s=1; for (m=1, 10^9, if(s!=(r=sigma(m)*omega(m)), s=r, write("b063071.txt", n++, " ", m - 1); if (n==100, break)) ) } \\ Harry J. Smith, Aug 16 2009

CROSSREFS

Cf. A001221, A002961, A000203.

Sequence in context: A349283 A333949 A002961 * A251963 A192007 A160682

Adjacent sequences: A063068 A063069 A063070 * A063072 A063073 A063074

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Aug 04 2001

STATUS

approved