A351553 Even numbers k such that there are no odd prime factors p of sigma(k) such that p does not divide A003961(k) and the valuation(k, p) is different from valuation(sigma(k), p), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

2, 6, 10, 14, 20, 22, 24, 28, 30, 34, 40, 42, 46, 54, 60, 62, 66, 70, 84, 94, 102, 106, 110, 114, 120, 130, 138, 140, 142, 154, 160, 168, 170, 174, 182, 186, 190, 198, 210, 214, 216, 220, 224, 230, 238, 254, 260, 264, 270, 280, 282, 290, 308, 310, 318, 322, 330, 340, 354, 374, 378, 380, 382, 390, 408, 410, 420, 426

Offset

1,1

Comments

Even numbers k for which A351555(k) = 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A351555(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); sum(k=1, #f~, if((f[k, 1]%2) && 0!=(u%f[k, 1]), (valuation(n, f[k, 1])!=f[k, 2]), 0)); };
isA351553(n) = (!(n%2) && 0==A351555(n));

Crossrefs

Cf. A000203, A005820, A003961, A046060, A351552.

Even terms in A351554, positions of zeros at even indices in A351555.

Cf. A351543 (complement among even numbers), A386430.

Sequence in context: A284678 A367367 A185548 * A354715 A239221 A039956

Adjacent sequences: A351550 A351551 A351552 * A351554 A351555 A351556

Keyword

nonn

Author

Antti Karttunen, Feb 16 2022

Extensions

Definition corrected by Antti Karttunen, Aug 27 2025

Status

approved