A342956 -id:A342956 - cp's OEIS frontend

A342957 a(n) is the least k such that A342956(k) = n.

1, 2, 4, 15, 39, 87, 183, 951, 1255, 1527, 3063, 15335, 12279, 61431, 49143, 516047, 491495, 1703767, 1310695, 8257487, 3145719, 15728631, 12582903, 94371815, 50331639, 352321527, 335544295

Offset: 0

J. M. Bergot and Robert Israel, Mar 30 2021

a(n) exists for all n, as A342956(2^(2^k)) = k+1.

If 2^n = p+q where p and q are primes, then A342956(p*q) = n so a(n) <= p*q <= 2^(2*n-2). Goldbach's conjecture implies such p and q exist for all n >= 2.

			a(3) = 15 because A342956(15) = 3 and this is the first appearance of the value 3 in A342956.

Cf. A342956.

f:= proc(n) local t; numtheory:-bigomega(add(t[1]*t[2], t=ifactors(n)[2])) end proc:
V:= Array(0..18): count:= 0:
for n from 0 while count < 19 do
v:= f(n):
if v <= 19 and V[v] = 0 then
    count:= count+1; V[v]:= n
fi
od:
convert(V,list);

Table[n=0;While[PrimeOmega[Plus@@Times@@@FactorInteger@++n]!=k];n,{k,0,14}] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

a(25)-a(26) from Chai Wah Wu, Mar 31 2021

A373976 a(n) = A001222(n) - A001222(A001414(n)), where A001222 is bigomega, the number of prime factors with multiplicity, and A001414 is sopfr, sum of prime factors with multiplicity. a(1) = 0 by convention.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 0, 1, 0, 3, 0, 1, -1, 2, 0, 0, -2, 3, 0, 0, 0, 1, 2, 0, 0, 4, 0, 0, -1, 2, 0, 3, -2, 3, 0, 1, 0, 1, 0, 0, 2, 3, -1, -1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, -1, 0, 0, 4, 1, 1, 0, 2, 0, -1, -3, 3, 0, 3, -1, 0, 0, 0, -2, 5, 0, -1, 2, 2, 0

Offset: 1

Antti Karttunen, Jun 24 2024

sign

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A001222, A001414, A342956.

Cf. also A045835.

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A373976(n) = if(1==n, 0, bigomega(n)-bigomega(A001414(n)));

a(n) = A001222(n) - A342956(n).

cp's OEIS Frontend

A342957 a(n) is the least k such that A342956(k) = n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica

Extensions

A373976 a(n) = A001222(n) - A001222(A001414(n)), where A001222 is bigomega, the number of prime factors with multiplicity, and A001414 is sopfr, sum of prime factors with multiplicity. a(1) = 0 by convention.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula